Set Covering Problem

In this paper we prove that the approximate solutions to the Min-Weighted Set Cover Problem provided by Chvatal's algorithm are combinatorially k-stable with respect to element insertions. Intuitively speaking, we define an approximate solution as combinatorially k-stable with respect to an update operation if its approximation ratio remains the same even if the problem instance is modified by any sequence of at most k such operations. This implies that, if no more than k updates are performed, the approximation ratio is preserved at no computational cost. In particular, we show that any solution returned by Chvatal's algorithm is combinatorially O(log m)-stable with respect to insertions, where m is the number of items in the instance. Hence, since the approximation ratio O(log m) is optimal, the best level of approximability is preserved.

We study an on-line model for set-covering implying that elements of the ground set of size n arrive one-by-one and with any such element σ i , arrive also the names of the sets containing it in the final instance. Any new element has to be processed irrevocably before the arrival of the next element. We study limits on the competitiveness of several greedy rules solving several alternatives of this basic model. For any of them we give lower and upper bounds for the competitive ratio achieved. We finally deal with the maximum budget saving problem. Here, an initial budget is allotted that is destined to cover the cost of an algorithm for solving set-covering and the objective is to maximize the savings on the initial budget. * A preliminary version of this paper, entitled Greedy algorithms for on-line set-covering and related problems has been included in the Proceedings of the 12th Computing: The Australasian Theory Symposium (CATS'06),

We study the following on-line model for set-covering: elements of a ground set of size n arrive one-by-one and with any such element ci, arrives also the name of some set Si0 containing ci and covering the most of the uncovered ground set- elements (obviously, these elements have not been yet revealed). For this model we analyze a simple greedy algorithm consisting of taking Si0 into the cover, only if ci is not already covered. We prove that the competitive ratio of this algorithm, that uses only O(log m) space, where m is the size of the set-system, is √ n and that it is asymptotically optimal for the model dealt, since no on-line algorithm can do better than p n/2. We next show that this model can also be used for solving minimum dominating set with competitive ratio bounded above by the square root of the size of the input graph. We also study a slightly simplified, but mo re memory consum- ing, on-line model: any time a ground set-element arrives, the whole sequence of the nam...

We study the following on-line model for set-covering: elements of a ground set of size n arrive one-by-one and with any such element ci, arrives also the name of some set Si0 containing ci and covering the most of the uncovered ground set-elements (obviously, these elements have not been yet revealed). For this model we analyze a simple greedy algorithm consisting of taking Si0 into the cover, only if ci is not already covered. We prove that the competitive ratio of this algorithm is p n and that it is asymptotically optimal for the model dealt, since no on-line algorithm can do better than p n=2. We next show that this model can also be used for solving minimum dominating set with competitive ratio bounded above by the square root of the size of the input graph. We nally deal with the maximum budget saving problem. Here, an initial budget is allotted that is destined to cover the cost of an algorithm for solving set-covering. The objective is to maximize the savings on the initial...

Metaheuristics are solution methods which combine local improvement procedures and higher level strategies for solving combinatorial and nonlinear optimization problems. In general, metaheuristics require an important amount of effort focused on parameter setting to improve its performance. In this work a 2-level metaheuristic approach is proposed so that Scatter Search and Ant Colony Optimization act as "low level" metaheuristics, whose parameters are set by a "higher level" Genetic Algorithm during execution, seeking to improve the performance and to reduce the maintenance. The Set Covering Problem is taken as reference since is one of the most important optimization problems, serving as basis for facility location problems, airline crew scheduling, nurse scheduling, and resource allocation.

We address a version of the set-cover problem where we do not know the sets initially (and hence referred to as covert) but we can query an element to find out which sets contain this element as well as query a set to know the elements. We want to find a small set-cover using a minimal number of such queries. We present a Monte Carlo randomized algorithm that approximates an optimal set-cover of size OP T within O(log N ) factor with high probability using O(OP T • log 2 N ) queries where N is the number of element in the universal set. We apply this technique to the network discovery problem that involves certifying all the edges and non-edges of an unknown n-vertices graph based on layered-graph queries from a minimal number of vertices. By reducing it to the covert set-cover problem we present an O(log 2 n)competitive Monte Carlo randomized algorithm for the covert version of network discovery problem. The previously best known algorithm has a competitive ratio of Ω( √ n log n) and therefore our result achieves an exponential improvement.

We present a new analysis of the greedy algorithm for the problem of finding a minimum spanning subset in ¢ -polymatroids. This algorithm has a performance ratio of approximately £ ¥¤ ¢ , which is best possible for large ¢ . A consequence of this algorithm is a polynomial time approximation algorithm with approximation ratio £ ¥¤ ¢ for finding minimum weight spanning subhypergraphs in ¦ ¢ ¨ § © -restricted hypergraphs. This generalization of the well-known set cover problem naturally arises when computing Steiner minimum trees. Other applications of the algorithm include the rigidity problem in statics.

Abstract: A new approach in the discrete optimization (partitioning and covering) problems is presented based on the expert knowledge presentations. An a priori uncertain information on the alternatives is given by some probability distribution and an a priori certain information on the knowledge competitions is given by some weights. A new criterion is introduced for a minimal fuzzy covering or partitioning problem which is a minimal value of average misbelief in possible alternatives. A bicriterial problem is obtained using the new criterion and the criterion of minimization of average price of the covering or partitioning. The proposed approach is illustrated by an example for the partitioning problem. Key–Words: Minimal fuzzy covering or partitioning, Minimal compatibility level, Positive and negative discrimination measures, Average misbelief criterion, Bicriterial problem 1

Mediator systems integrate distributed, heterogeneous and autonomous data sources, but their e ective use requires the solution of hard query optimization problems. This is usually done in one of two w ays: when the set of data sources is xed, their ordering into a feasible and e cient query is treated as a join order problem when the set is not known, their selection from a superset is treated as a set covering problem. This two-phase approach is unlikely to nd optimum queries, and we describe a generalised approach in which a feasible query is constructed from a subset of the available data sources. Under simple cost assumptions this can be encoded and solved as a SAT problem. Results on arti cial benchmarks indicate that this is an interesting problem, with a combination of features that make it hard for both complete and incomplete search. We investigate both types of algorithm and a hybrid approach, with and without symmetry breaking constraints. The bestcombination turns out to behybrid search without symmetry breaking.

We give an efficient deterministic parallel approximation algorithm for the minimumweight vertex-and set-cover problems and their duals (edge/element packing). The algorithm is simple and suitable for distributed implementation. It fits no existing paradigm for fast, efficient parallel algorithms -it uses only "local" information at each step, yet is deterministic. (Generally, such algorithms have required randomization.) The result demonstrates that linear-programming primal-dual approximation techniques can lead to fast, efficient parallel algorithms. The presentation does not assume knowledge of such techniques.

The Set Covering problem is one the of most important NP-complete 0-1 integer programming problems because it serves as a model for many real world problems like the crew scheduling problem, facility location problem, vehicle routing etc. In this paper, an algorithm is suggested to solve a multi objective Set Covering problem with fuzzy linear fractional functionals as the objectives. The algorithm obtains the complete set of efficient cover solutions for this problem. It is based on the cutting plane approach, but employs a more generalized and a much deeper form of the Dantzig cut. The fuzziness in the problem lies in the coefficients of the objective functions. In addition, the ordering between two fuzzy numbers is based on the possibility and necessity indices introduced by Dubois and Prade [Ranking fuzzy numbers in the setting of possibility theory. Inf. Sci. 30 (1983) 183-224.]. Our aim is to develop a method which provides the decision maker with a fuzzy solution. An illustrative numerical example is elaborated to clarify the theory and the solution algorithm.

Motivated by the widespread proliferation of wireless networks employing directional antennas, we study some capacitated covering problems arising in these networks. Geometrically, the area covered by a directional antenna with parameters α, ρ, r is a set of points with polar coordinates (r, θ) such that r ≤ r and α ≤ θ ≤ α + ρ. Given a set of customers, their positions on the plane and their bandwidth demands, the capacitated covering problem considered here is to cover all the customers with the minimum number of directional antennas such that the demands of customers assigned to an antenna stays within a bound. We consider two settings of this capacitated cover problem arising in wireless networks. In the first setting where the antennas have variable angular range, we present an approximation algorithm with ratio 3. In the setting where the angular range of antennas is fixed, we improve this approximation ratio to 1.5. These results also apply for a related problem of bin packing with deadlines. In this problem we are are given a set of items, each with a weight, arrival time and deadline, and we want to pack each item into a bin after it arrives but before its deadline. The objective is to minimize the number of bins used. We present a 3-approximation algorithm for this problem, and 1.5-approximation algorithm for the special case when each difference between a deadline and the corresponding arrival time is the same.

Metaheuristics are solution methods which combine local improvement procedures and higher level strategies for solving combinatorial and nonlinear optimization problems. In general, metaheuristics require an important amount of effort focused on parameter setting to improve its performance. In this work a 2-level metaheuristic approach is proposed so that Scatter Search and Ant Colony Optimization act as "low level" metaheuristics, whose parameters are set by a "higher level" Genetic Algorithm during execution, seeking to improve the performance and to reduce the maintenance. The Set Covering Problem is taken as reference since is one of the most important optimization problems, serving as basis for facility location problems, airline crew scheduling, nurse scheduling, and resource allocation.

We present new combinatorial approximation algorithms for k-set cover. Previous approaches are based on extending the greedy algorithm by efficiently handling small sets. The new algorithms further extend them by utilizing the natural idea of computing large packings of elements into sets of large size. Our results improve the previously best approximation bounds for the k-set cover problem for all values of k ≥ 6. The analysis technique could be of independent interest; the upper bound on the approximation factor is obtained by bounding the objective value of a factor-revealing linear program.

In many situations, cooperating agents have different status with respect to an activity. Often a coalition can undertake the activity only if sufficiently many agents, or agents of sufficient seniority participate in it. The concept of a simple game, introduced by von Neumann & Morgenstern (1944), is flexible enough to model a large class of such situations. In this dissertation, we consider two important classes of simple games called the classes of weighted simple games,

We address the problem of instruction selection in code generation for embedded DSP microprocessors. Such processors have highly irregular data-paths, and conventional code generation methods typically result in inefficient code. Instruction selection can be formulated as directed acyclic graph (DAG) covering. Conventional methods for instruction selection use heuristics that break up the DAG into a forest of trees and then cover them independently. This breakup can result in suboptimal solutions for the original DAG. Alternatively, the DAG covering problem can be formulated as a binate covering problem, and solved exactly or heuristically using branch-andbound methods. We show that optimal instruction selection on a DAG in the case of accumulator-based architectures requires a partial scheduling of nodes in the DAG, and we augment the binate covering formulation to minimize spills and reloads. We show how the irregular data transfer costs of typical DSP data-paths can be modeled in the binate covering formulation.

Set covering problem is the model for many important industrial applications. In this paper, we solve some benchmarks of this problem with ant colony optimization algorithms using a new transition rule. A look-ahead mechanism was incorporated to check constraint consistency in ant computing. Computational results are presented showing the advantages to use this additional mechanism to ant system and ant colony system.

The recent requirement for increased speed in the design and manufacturing of new products led to a rapid evolution of the technics for fast production (rapid prototyping, machining at high speed, etc.). But a significant component did not follow this evolution, that is the dimensional and functional checking process, which is most of the time carried out in a traditional way. The use of range sensor allows very significant improvement in acquisition speed but does not equal the accuracy obtained with a coordinate measuring machine. In order to obtain a quality control close to that obtained in metrology, we suggest to improve the accuracy of the depth measurements by following an acquisition strategy. We propose in this paper such a strategy to automatically produce a sensing plan for completely and precisely acquiring the geometry of a surface or of a complete piece whenever possible. The system requires the exact position and orientation of the part and its CAD model in IGES format. There is no limitation regarding the shape of the part to be digitized. A Biris sensor was used, and for this sensor, the precision of the 3D measured points is function of the distance and of the incident angle with which the laser beam reaches the surface. Our strategy guaranties that the viewpoint found meets the best precision conditions in the scanning process.

This document is the author's post-print version, incorporating any revisions agreed during the peer-review process. Some differences between the published version and this version may remain and you are advised to consult the published version if you wish to cite from it.

We introduce the notion of T -path within Petri nets, and propose a simple approach, based on previous work developed for directed hypergraphs, in order to determine structural properties of nets; in particular, we study the relationships between T -paths in a Petri net and firable sequences of transitions. Let us consider a net P = P, T, A, M 0 and the set of places with a positive marking in M 0 , i.e., P 0 = {p | M 0 (p) > 0}. If we regard the net as a directed graph, the existence of a simple path from any place in P 0 to a transition t is, of course, a necessary condition for the potential firability of t. This is sufficient only if the net is a State Machine, where In this paper we show that the existence of a T -path from any subset of P 0 to a transition t is a more restrictive condition and is, again, a necessary condition for the potential firability of t. But, in this case: (a) if P is a Conflict Free Petri net, this is also a sufficient condition, (b) if P is a general Petri net, t is potentially firable by increasing the number of tokens in P 0 . For Conflict-Free nets (CFPN) we consider the following problems: (a) determining the set of firable transitions, (b) determining the set of reachable places, (c) determining the set of live transitions, (d) deciding the boundedness of the net. For all these problems we provide algorithms requiring linear space and time, i.e., O(|A| + |P | + |T |), for a net P = P, T, A, M 0 . Previous results for this class of networks are given by Howell, Rosier and Yen [18], providing algorithms for solving problems in Conflict-Free nets in O(|P |×|T |) time and space. Given a Petri net and a marking M , the well known coverability problem consists in finding a reachable marking M such that M ≥ M ; this problem is known to be EXPSPACE-hard . For general Petri nets we provide a partial answer to this problem. M is coverable by augmentation if it is coverable from an augmented marking M 0 of the initial marking M 0 : M 0 ≥ M 0 and, for all p ∈ P , M 0 (p) = 0 if M 0 (p) = 0. We solve this problem in linear time. The algorithms to compute T -paths are incremental: it is possible to modify the network (adding new places, transitions, arcs, tokens), and update the set of potentially firable transitions and reachable places without recomputing them from scratch. This feature results meaningful when used during the interactive design of a system.

Perkembangan ekonomi dan industri di kota Bandar Lampung dapat di kategorikan cepat, Bandar Lampung sebagai ibukota provinsi memiliki jumlah penduduk yang mengalami peningkatan dari tahun ke tahun dengan jumlah total penduduk 902.885 jiwa di tahun 2012 dan 1.167.101 jiwa di tahun 2014. Dengan meningkatnya jumlah penduduk dari tahun ke tahun menyebabkan meningkatkan pula jumlah kebutuhan barang di kota Bandar lampung. Tujuan dilakukannya penelitian ini adalah untuk mengetahui bagaimana karateristik tarikan pergerakan dan mengetahui variable yang paling berpengaruh terhadap tarikan barang di Bandar Lampung. Penelitian ini dilakukan dengan menggunakan analisis regresi linier berganda dengan bantuan program SPSS metode stepwise, dengan delapan variabel yaitu jumlah penduduk (X1), jumlah keluarga sejahtera (X2), jumlah perusahaan (X3), jumlah minimarket (X4), produksi tanaman sayur (X5), produksi tanaman buah-buahan (X6), produksi tanaman perkebunan rakyat (X7), produksi tanaman pangan (...

We present construction of the 3 and 4 dimensional grids in the parameter space for all sky-search of gravitational wave signals from white dwarf binaries with LISA data. The 3 dimensional grid is for search of frequency and the sky position of the source and the 4 dimensional grid includes the spin down parameter. The grid solves the covering problem in the parameter space with the constraint that nodes of the grid coincide with Fourier frequencies (multiples of the inverse of the observation time).This allows the use of the fast Fourier transform (FFT) in the evaluation of the optimal statistic and greatly speeds up the search.

Routing problems have been considered as central problems in the fields of transportation, distribution and logistics. LS(Graph) is a generic framework allowing to model and solve constrained optimum paths problems on graphs by local search where paths are known to be elementary (i.e., edges, vertices cannot be repeated on paths). In many real-world situations, the paths to be determined are not known to be neither simple nor elementary. In this paper, we extend the LS(Graph) framework by designing and implementing abstractions that allow to model and solve constrained paths problem where edges, vertices can be repeated on paths (call non-simple paths). We also propose an instance of such problem class: the routing for network covering (RNC) problem which arises in the context of rescue after a natural disaster in which we have to route a fleet of identical vehicles with limited capacity on a transportation network in order to collect the informations of the disaster. Given an undirected weighted graph G = (V, E) representing a transportation network and a vertex v0 ∈ V representing the depot, the RNC problem consists of routing a fleet of unlimited number of identical vehicles with limited capacity that cannot perform a path of length > L such that each vehicle starts from and teminates at the depot and all the edges of a given set S (S ⊆ E) must be visited. The objective of the routing plan is to minimize the number of vehicles used. This paper discusses the challenge around this problem and applies the constructed framework to the Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.

The Multidimensional Knapsack/Covering Problem (KCP) is a 0-1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP.

Elektrikli ve elektronik cihazlar (e-eşya), kullanım ömürleri tamamlandığında elektrikli ve elektronik atığa (AEEE) dönüşmektedir. AEEE'ler atıldıklarında, yakıldıklarında veya geri dönüşüm için parçalandıklarında tehlikeli maddeler içeren ürünlere dönüşerek çevreye ve insan sağlığına zarar vermektedir. AEEE'lerin zararlarını en aza indirmek ve geri dönüşümlerinden ekonomik fayda sağlamak amacıyla belediyeler tarafından uygun şekilde toplanması, taşınması ve işlenmesi gerekmektedir. Bu çalışmada, Çankaya İlçesi Çevre Koruma ve Kontrol Müdürlüğü işbirliği ile Çankaya Belediyesi için AEEE yönetimine destek olacak bir çalışma gerçekleştirilmiştir. Çalışma kapsamında ilk olarak Çankaya ilçesi için AEEE miktarları televizyon, buzdolabı, çamaşır makinesi, fırın ve elektrikli süpürge için kullanıcı davranışları dikkate alınarak tahmin edilmiştir. Daha sonra AEEE toplama noktalarının belirlenmesi için yer seçimi problemi bir küme örtme problemi olarak ele alınmış ve çözülmüştür. Electrical-electronic waste (WEEE) is generated from electric and electronic devices at the end of their lifecycles. When WEEEs are disposed, burned or disassembled for recycling, they are transformed into products containing hazardous substances and harm the environment and human health. Therefore WEEEs should be collected, transported and processed properly during their recycling operations by municipality authority in order to minimize their damage and maximize their economic benefit. In this paper, a study is carried out for the WEEE management of Çankaya Municipality by the cooperation of Environmental Conservation and Control Department of Çankaya. For this purpose first WEEE with a focus on television, refrigerator, washing machine, oven and vacuum cleaner are estimated based on the electronic device usage behavior of residents in Çankaya. Secondly, the WEEE collection points' location problem is solved considering set covering problem.

The hub location problem appears in a variety of applications including airline systems, cargo delivery systems, and telecommunication network design. When we analyze hub location applications separately, we observe that each area has its own characteristics. In this paper, we study the single allocation hub covering problem under capacity constraints (or CSAHCLP-Capacitate Single Allocation Hub Covering Location Problem) over complete hub networks and propose a mixed-integer programming formulation to this end. The aim of our model is to find the location of hubs and allocate nonhub nodes to the located hub nodes so much that the travel cost between any hub-node pair is within a given cost bound and hubs are considered under capacity constraint. Unlike [1] we prepare new formulation with covering radius. In general this paper attempts to propose a new mixed-integer programming formulation and adapt the imperialist competitive algorithm to solve the hub covering location problem. Also unlike previous studies, we adapt new solution algorithm (Imperialist competitive algorithm) for solving our problem that has not used yet.

In this paper, we take a close look at the problem of learning simple neural concepts under the uniform distribution of examples. By simple neural concepts we mean concepts that can be represented as simple combinations of perceptrons (halfspaces). One such class of concepts is the class of halfspace intersections. By formalizing the problem of learning halfspace intersections as a set covering problem, we are led to consider the following sub-problem: given a set of non linearly separable examples, find the largest linearly separable subset of it. We give an approximation algorithm for this NP-hard sub-problem. Simulations, on both linearly and non linearly separable functions, show that this approximation algorithm works well under the uniform distribution, outperforming the Pocket algorithm used by many constructive neural algorithms. Based on this approximation algorithm, we present a greedy method for learning halfspace intersections. We also present extensive numerical results that strongly suggests that this greedy method learns halfspace intersections under the uniform distribution of examples. Finally, we introduce a new class of simple, yet very rich, neural concepts that we call neural decision lists. We show how the greedy method can be generalized to handle this class of concepts. Both greedy methods for halfspace intersections and neural decision lists were tried on real-world data with very encouraging results. This shows that these concepts are not only important from the theoretical point of view, but also in practice.

The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, for example buses, trains, plane or boat drivers or pilots, for the transportation of passengers or goods. This is a complex problem because it involves several constraints related to labour and company rules and can also present different evaluation criteria and objectives. Being able to develop an adequate model for this problem that can represent the real problem as close as possible is an important research area. The main objective of this research work is to present new mathematical models to the DSP problem that represent all the complexity of the drivers scheduling problem, and also demonstrate that the solutions of these models can be easily implemented in real situations. The most well-known and general formulation for the DSP is a Set Partition/Set Covering Model (SPP/SCP). However, to a large extend these models simplify some of the specific business aspects and issues of real problems. This makes it difficult to use these models as automatic planning systems because the schedules obtained must be modified manually to be implemented in real situations. Based on extensive passenger transportation experience in bus companies in Portugal, we propose new alternative models to formulate the DSP problem. These models are also based on Set Partitioning/Covering Models; however, they take into account the bus operator issues and the perspective opinions and environment of the user. We follow the steps of the Operations Research Methodology which consist of: Identify the Problem; Understand the System; Formulate a Mathematical Model; Verify the Model; Select the Best Alternative; Present the Results of the Analysis and Implement and Evaluate. All the processes are done with close participation and involvement of the final users from different transportation companies. The planner's opinion and main criticisms are used to improve the proposed model in a continuous enrichment process.

Promising a suitable coverage is one of the problems in Wireless Sensor Network where a random deployment make it very difficult to measure. In this paper, a novel equation base on Gaussian distribution is proposed to estimate the deployment density. This function uses the a-Covering value and coverage percentage as inputs. Simulation results show high correlation between proposed equation and simulation data. Moreover, the average of the error in different scenarios is 0.38%.

Recently a novel technique has been published to augment traditional Branchand-Bound (B&B) while solving exactly a discrete optimization problem [Goldberg et al., 1997]. This technique is based on the negative thinking paradigm and has been applied to develop dramatic impact of the negative thinking paradigm in searching the solution space and propose ¡ £ as the most efficient available tool for unate covering.

The NP-hard Max-Cover problem requires selecting sets from a collection so as to maximize the size of the union. This classic problem occurs commonly in many settings in web search and advertising. For moderately-sized instances, a greedy algorithm gives an approximation of (1 − 1/). However, the greedy algorithm requires updating scores of arbitrary elements after each step, and hence becomes intractable for large datasets. We give the first max cover algorithm designed for today's large-scale commodity clusters. Our algorithm has provably almost the same approximation as greedy, but runs much faster. Furthermore, it can be easily expressed in the Map-Reduce programming paradigm, and requires only polylogarithmically many passes over the data. Our experiments on five large problem instances show that our algorithm is practical and can achieve good speedups compared to the sequential greedy algorithm.

Our starting point is an algorithm of Kenyon, Randall, and Sinclair, which is built upon the ideas of Jerrum and Sinclair, giving an approximation to crucial parameters of the monomer-dimer covering problem in polynomial time. We make two key improvements to their algorithm: we greatly reduce the number of simulations that must be run by estimating good values of the generating function parameter, and we greatly reduce the number of steps that must be taken in each simulation by aggregating to a simulation with at most five states. The result is an algorithm that is computationally feasible for modestly sized meshes. We use our algorithm on two-and three-dimensional problems, computing approximations to the coefficients of the generating function and some limiting values.

The paper deals with an original approach to scan path planning that applies for any type of sensors. The approach relies on the representation of the part surface as a voxel map. The size of each voxel is defined according to the sensor FOV. To each voxel, a unique point of view is associated in function of visibility and quality criteria. Whatever the sensor, the method provides a set of admissible points of view to ensure the surface digitizing with a given quality.

This growing e-commerce poses a huge challenge for the last mile delivery services. Currently, most of the deliveries are performed at customer's home and workplace where customers wait to get their online orders. Recently companies like Amazon and FedEx developed locker delivery. When customers shop online, they can choose a nearby locker as their pickup location. In the past two years, a new concept called trunk delivery has been proposed. Here, customers' orders can be delivered to the trunks of their cars. Volvo launched its world-first in-car delivery service in Sweden in 2016. The courier has a one-time digital code to get access to the car. Trunk delivery is different from home delivery and locker delivery since the car moves and may be in different locations during different periods of time. As a consequence, synchronization between the car and the courier is required to perform the delivery. This work studies a last-mile system that combines home/workplace, locker and car trunk delivery services. We call the resulting problem the generalized vehicle routing problem with time windows (GVRPTW). This work aims to develop an efficient solving method for the GVRPTW. This work follows a work from the authors where an efficient branch-and-cut algorithm for the one vehicle case has been developed [4].

We study the following on-line model for set-covering: elements of a ground set of size n arrive one-by-one and with any such element ci, arrives also the name of some set Si0 containing ci and covering the most of the uncovered ground set- elements (obviously, these elements have not been yet revealed). For this model we analyze a simple greedy

The covering problem of a three dimensional body using different radius spheres is considered. The motivating application - the treatment planning of Gamma Knife radiosurgery - is briefly discussed. We approach the problem only by the geometric covering point of view, that is, given a set of spheres and a body, the objective is to cover the body using the smallest possible number of spheres, regardless of the dosage issue. In order to solve this mathematical programming problem, we consider an approach based on the application of penalty and stochastic local search techniques. Finally, some illustrative results and comparisons are presented.

Due to an oversight on the part of the authors, the proof given in [1] for The W T Two-Pair Theorem is incomplete, and should be replaced with the following proof. Recall that a two-pair is a pair o f non-adjacent vertices in a graph, such that every chordless path between the two vertices has exactly two edges.

The set k-covering problem is a variant of the classical set covering problem, in which each object is required to be covered at least k times. We describe a hybrid Lagrangean heuristic, named LAGRASP, which combines subgradient optimization and GRASP with path-relinking to solve the set kcovering problem. Computational experiments carried out on 135 test instances show experimentally that by properly tuning the parameters of LAGRASP, it is possible to obtain a good trade-off between solution quality and running times. Furthermore, LAGRASP makes better use of the dual information provided by subgradient optimization and is able to discover better solutions and to escape from locally optimal solutions even after the stabilization of the lower bounds, whereas other strategies fail to find new improving solutions. Keywords GRASP • hybrid heuristics • metaheuristics • path-relinking • Lagrangean relaxation • Lagrangean heuristics • local search • set covering • set multicovering • set k-covering.

The set multicovering or set k-covering problem is an extension of the classical set covering problem, in which each object is required to be covered at least k times. The problem finds applications in the design of communication networks and in computational biology. We describe a GRASP with pathrelinking heuristic for the set k-covering problem, as well as the template of a family of Lagrangean heuristics. The hybrid GRASP Lagrangean heuristic employs the GRASP with path-relinking heuristic using modified costs to obtain approximate solutions for the original problem. Computational experiments carried out on 135 test instances show experimentally that the Lagrangean heuristics performed consistently better than GRASP. By properly tuning the parameters of the GRASP Lagrangean heuristic, it is possible to obtain a good trade-off between solution quality and running times. Furthermore, the GRASP Lagrangean heuristic makes better use of the dual information provided by subgradient optimization and is able to discover better solutions and to escape from locally optimal solutions even after the stabilization of the lower bounds, when other strategies fail to find new improving solutions.

We compare several ways to model a habitat reserve site selection problem in which an upper bound on the total area of the selected sites is included. The models are cast as optimization coverage models drawn from the location science literature. Classic covering problems typically include a constraint on the number of sites that can be selected. If potential reserve sites vary in terms of area, acquisition cost or land value, then sites need to be differentiated by these characteristics in the selection process. To address this within the optimization model, the constraint on the number of selected sites can either be replaced by one limiting the total area of the selected sites or area minimization can be incorporated as a second objective. We show that for our dataset and choice of optimization solver average solution time improves considerably when an area-constrained reserve site selection problem is modeled as a two objective rather than a single objective problem with a constraint limiting the total area of the selected sites. Computational experience is reported using a large dataset from Australia.

The NP-hard Max-Cover problem requires selecting sets from a collection so as to maximize the size of the union. This classic problem occurs commonly in many settings in web search and advertising. For moderately-sized instances, a greedy algorithm gives an approximation of (1 − 1/). However, the greedy algorithm requires updating scores of arbitrary elements after each step, and hence becomes intractable for large datasets. We give the first max cover algorithm designed for today's large-scale commodity clusters. Our algorithm has provably almost the same approximation as greedy, but runs much faster. Furthermore, it can be easily expressed in the Map-Reduce programming paradigm, and requires only polylogarithmically many passes over the data. Our experiments on five large problem instances show that our algorithm is practical and can achieve good speedups compared to the sequential greedy algorithm.

We consider the problem of visualizing the evolution of tags within the Flickr (flickr.com) online image sharing community. Any user of the Flickr service may append a tag to any photo in the system. Over the past year, users have on average added over a million tags each week. Understanding the evolution of these tags over time is therefore a challenging task. We present a new approach based on a characterization of the most interesting tags associated with a sliding interval of time. An animation provided via Flash in a Web browser allows the user to observe and interact with the interesting tags as they evolve over time. New algorithms and data structures are required to support the efficient generation of this visualization. We combine a novel solution to an interval covering problem with extensions to previous work on score aggregation in order to create an efficient backend system capable of producing visualizations at arbitrary scales on this large dataset in real time.

Evolutionary algorithms have been used to solve several optimization problems, showing an efficient performance. Nevertheless, when these algorithms are applied they present the difficulty to decide on the appropriate values of their parameters. Typically, parameters are specified before the algorithm is run and include population size, selection rate, and operator probabilities. This process is known as offline control and is even considered as an optimization problem in itself. On the other hand, parameter settings or control online is a variation of the algorithm original version. The main idea is to vary the parameters so that the algorithm of interest can provide the best convergence rate and thus may achieve the best performance. In this paper, we propose an adaptive black hole algorithm able to dynamically adapt its population according to solving performance. For that, we use autonomous search which appeared as a new technique that enables the problem solver to control and a...

We previously showed the feasibility of a fault detection scheme for all-optical networks (AONs) based on their decomposition into monitoring-cycles (m-cycles). In this paper, an m-cycle construction for fault detection is formulated as a cycle cover problem with certain constraints. A heuristic spanning-tree based cycle construction algorithm is proposed and applied to four typical networks: NSFNET, ARPA2, SmallNet, and Bellcore. Three metrics: grade of fault localization, wavelength overhead, and the number of cycles in a cover are introduced to evaluate the performance of the algorithm. The results show that it achieves nearly optimal performance.

denotes the vector with m ones. A set-covering problem is regular if there exists an ordering of the variables u = (x1,.. . , x,,) such that, for every feasible solution x with Xi = 1, Xj = 0, j < i, the vector x + ej-ej is also a feasible solution, where ej is the ith unit vector. The matrix M of a regular set-covering problem is said to be regular. A regular clutter is any clutter whose incidence matrix is regular. In this paper we describe some properties of regular clutters and propose an algorithm which, in 0(mn) steps, generates all the minimal transversals of a regular clutter L and produces the transversal having minimum weight.

SNPs are positions of the DNA sequences where the differences among individuals are embedded. The knowledge of such SNPs is crucial for disease association studies, but even if the number of such positions is low (about 1% of the entire sequence), the cost to extract the complete information is actually very high. Recent studies have shown that DNA sequences are structured into blocks of positions, that are conserved during evolution, where there is strong correlation among values (alleles) of different loci. To reduce the cost of extracting SNPs information, the block structure of the DNA has suggested to limit the process to a subset of SNPs, the so-called Tag SNPs, that are able to maintain the most of the information contained in the whole sequence. In this paper, we apply a technique for feature selection based on integer programming to the problem of Tag SNP selection. Moreover, to test the quality of our approach, we consider also the problem of SNPs reconstruction, i.e. the problem of deriving unknown SNPs from the value of Tag SNPs and propose two reconstruction methods, one based on a majority vote and the other on a machine learning approach. We test our algorithm on two public data sets of different nature, providing results that are, when comparable, in line with the related literature. One of the interesting aspects of the proposed method is to be found in its capability to deal simultaneously with very large SNPs sets, and, in addition, to provide highly informative reconstruction rules in the form of logic formulas.

In this paper we investigate logic classification and related feature selection algorithms for large biomedical data sets. When the data is in binary/logic form, the feature selection problem can be formulated as a Set Covering problem of very large dimensions, whose solution is computationally challenging. We propose an alternative approximated formulation for feature selection that results in an extension of Set Covering of compact size, and use the logic classifier Lsquare to test its performances on two wellknown data sets. An ad hoc metaheuristic of the GRASP type is used to solve efficiently the feature selection problem. A simple and effective method to convert rational data into logic data by interval mapping is also described. The computational results obtained are promising and the use of logic models, that can be easily understood and integrated with other domain knowledge, is one of the major strengths of this approach.

We propose a moment relaxation for two problems, the separation and covering problem with semi-algebraic sets generated by a polynomial of degree d. We show that (a) the optimal value of the relaxation finitely converges to the optimal value of the original problem, when the moment order r increases and (b) there exist probability measures such that the moment relaxation is equivalent to the original problem with r = d. We further provide a practical iterative algorithm that is computationally tractable for large datasets and present encouraging computational results.

Abstract: Motivated by a novel application of description logics in the area ofelectronic commerce, this paper investigates a new instance of the problemof rewriting concepts using terminologies, namely the best covering problem:given a concept description Q and a terminology T , the problem consists innding a rewriting of Q that uses only concept names from T and containsas much as

In this paper we consider a set of origin-destination pairs in a mixed model in which a network embedded in the plane represents an alternative high-speed transportation system, and study a trip covering problem which consists on locating two points in the network which maximize the number of covered pairs, that is, the number of pairs which use the network by acceding and exiting through such points.