Polynomial-time algorithm

Abstract. Coverage is an important issue in Wireless Sensors Networks (WSNs). It gives a measure of the quality of surveillance a WSN provides over a field it is designed to monitor. Different measures of cover-age capture different aspects of surveillance. In this paper, we study two ...

This paper introduces the maximization version of the kpath vertex cover problem, called the Maximum k-Path Vertex Cover problem (MaxP k VC for short): A path consisting of k vertices, i.e., a path of length k -1 is called a k-path. If a k-path P k includes a vertex v in a vertex set S , then we say that v or S covers P k . Given a graph G = (V, E) and an integer s, the goal of MaxP k VC is to find a vertex subset S ⊆ V of at most s vertices such that the number of k-paths covered by S is maximized. The problem MaxP k VC is generally NP-hard. In this paper we consider the tractability/intractability of MaxP k VC on subclasses of graphs. We prove that MaxP 3 VC remains NP-hard even for split graphs. Furthermore, if the input graph is restricted to graphs with constant bounded treewidth, then MaxP 3 VC can be solved in polynomial time.

We define extended conflict free dependencies in the context of functional and multivalued dependencies, and prove that there exists an acyclic, dependency preserving, 4NF database scheme if and only if the given set of dependencies has an extended conflict free cover. This condition can be checked in polynomial time. A polynomial time algorithm to obtain such a scheme for a given extended conflict free set of dependencies is also presented. The result is also applicable when the data dependencies consists of only functional dependencies, giving the necessary and sufficient condition for an acyclic, dependency preserving BCNF database scheme

We present results on two classes of problems. The first result addresses the long standing open problem of finding unifying principles for Linkage Disequilibrium (LD) measures in population genetics (Lewontin 1964 [10], Hedrick 1987 [8], Devlin and Risch 1995 [5]). Two desirable properties have been proposed in the extensive literature on this topic and the mutual consistency between these properties has remained at the heart of statistical and algorithmic difficulties with haplotype and genome-wide association study analysis. The first axiom is (1) The ability to extend LD measures to multiple loci as a conservative extension of pairwise LD. All widely used LD measures are pairwise measures. Despite significant attempts, it is not clear how to naturally extend these measures to multiple loci, leading to a "curse of the pairwise". The second axiom is (2) The Interpretability of Intermediate Values. In this paper, we resolve this mutual consistency problem by introducing a new LD measure, directed informativeness -→ I (the directed graph theoretic counterpart of the informativeness measure introduced by Halldorsson et al. [6]) and show that it satisfies both of the above axioms. We also show the maximum informative subset of tagging SNPs based on -→ I can be computed exactly in polynomial time for realistic genome-wide data. Furthermore, we present polynomial time algorithms for optimal genome-wide tagging SNPs selection for a number of commonly used LD measures, under the bounded neighborhood assumption for linked pairs of SNPs. One problem in the area is the search for a quality measure for tagging SNPs selection that unifies the LD-based methods such as LD-select (implemented in Tagger, de Bakker et al. 2005 [4], Carlson et al. 2004 [3]) and the information-theoretic ones such as informativeness. We show that the objective function of the LD-select algorithm is the Minimal Dominating Set (MDS) on r 2 -SNP graphs and show that we can compute MDS in polynomial time for this class of graphs. Although

Threshold logic is gaining prominence as an alternative to Boolean logic. The main reason for this trend is the availability of devices that implement these circuits efficiently (current mode, differential mode circuits), as well as the promise they hold for the future nano devices (RTDs, SETs, QCAs and other nano devices). This has generated renewed interest in the design automation community to design efficient CAD tools for threshold logic. Recently a lot of work has been done to synthesize threshold logic circuits. So far there has been no efficient method to verify the synthesized circuits. In this work we address the problem of combinational equivalence checking for threshold circuits. We propose a new algorithm, to obtain compact functional representation of threshold elements. We give the proof of correctness, and analyze its runtime complexity. We use this polynomial time algorithm to develop a new methodology to verify threshold circuits. We report the result of our experiments, comparing the proposed methodology to the naive approach. We get up to 189X improvement in the run time (23X on average), and could verify circuits that the naive approach could not.

In this paper, we study exact learnability of bounded-width ordered binary decision diagrams (OBDDs) when no ordering of the variables is given and learning is conducted by way of equivalence queries and membership queries. We present a learning algorithm for width-2 OBDDs, an algorithm which uses O(n 3 ) equivalence queries alone, where n is the number of variables. We also present a learning algorithm for width-2 OBDDs that uses O(n) proper equivalence queries and O(n 2 ) membership queries. Further, we show a negative result: that there are no polynomial-time algorithms capable of learning width-3 OBDDs from proper equivalence queries alone.

Stochastic optimization is a leading approach to model optimization problems in which there is uncertainty in the input data, whether from measurement noise or an inability to know the future. In this survey, we outline some recent progress in the design of polynomialtime algorithms with performance guarantees on the quality of the solutions found for an important class of stochastic programming problems -2-stage problems with recourse. In particular, we show that for a number of concrete problems, algorithmic approaches that have been applied for their deterministic analogues are also effective in this more challenging domain. More specifically, this work highlights the role of tools from linear programming, rounding techniques, primal-dual algorithms, and the role of randomization more generally.

Design of cellular networks has drawn much recent interest from the OR scientific community. A challenging issue is the handling of channel interference constraints. Co-channel interference occurs when the same channel is reused within a threshold distance. Adjacent-channel interference occurs when two channels with adjacent or nearby frequencies are used in the same cell tower. We present a mathematical programming formulation for this channel allocation problem with both types of interference constraints-it also includes decisions on location of cell towers. Our focus is on the special case where a cell tower and/or channel can interfere with at most two other towers/channels. By establishing theoretical properties for channel allocation amongst towers under this circumstance, we develop an efficient solution procedure. An iteration of the procedure uses a heuristic to locate the cell towers, then allocates the channels to the towers using a polynomial-time algorithm, and finally improves this allocation using a simulated annealing procedure. The iterative steps are embedded within an external simulated annealing method. This nested simulated annealing procedure provides encouraging computational results compared to a standard commercial solver like ILOG CPLEX 8.1. The major contribution of the work is the simultaneous consideration of co-channel and adjacent-channel interference constraints.

Design of cellular networks has drawn much recent interest from the OR scientific community. A challenging issue is the handling of channel interference constraints. Co-channel interference occurs when the same channel is reused within a threshold distance. Adjacent-channel interference occurs when two channels with adjacent or nearby frequencies are used in the same cell tower. We present a mathematical programming formulation for this channel allocation problem with both types of interference constraints-it also includes decisions on location of cell towers. Our focus is on the special case where a cell tower and/or channel can interfere with at most two other towers/channels. By establishing theoretical properties for channel allocation amongst towers under this circumstance, we develop an efficient solution procedure. An iteration of the procedure uses a heuristic to locate the cell towers, then allocates the channels to the towers using a polynomial-time algorithm, and finally improves this allocation using a simulated annealing procedure. The iterative steps are embedded within an external simulated annealing method. This nested simulated annealing procedure provides encouraging computational results compared to a standard commercial solver like ILOG CPLEX 8.1. The major contribution of the work is the simultaneous consideration of co-channel and adjacent-channel interference constraints.

In context-aware route planning, a set of agents has to plan routes on a common infrastructure and each agent has to plan a conflict-free route from a source to a destination with- out invalidating plans made by other agents. The existence of such a conflict-free set of plans can be ensured if each agent is allowed to reserve time slots

We introduce an algorithm for cooperative planning in multi-agent systems. The algorithm enables the agents to combine (fuse) their plans in order to increase their joint profits. A computational resources and skills framework is developed for representing the planned activities of an agent under time constraints. Using this resource-skill framework, we present an efficient (polynomial time) algorithm that fuses the plans of a group of agents in such a way that their joint profits improve. The framework and the algorithm are illustrated ...

Since summer 2007, mobile phone users in the European Union (EU) are protected by a ceiling on the roaming tariff when calling or receiving a call abroad. We analyze the effects of this price regulative policy, and compare it to alternative implementations of price regulations. The problem is a three-level mathematical program: The EU determines the price regulative policy that maximizes overall social welfare, the telephone operator sets profit-maximizing prices, and customers choose to accept or decline the operator's offer. The first part of this paper contains a polynomial time algorithm to solve such a threelevel program. The crucial idea is to partition the polyhedron of feasible price regulative parameters into a polynomial number of smaller polyhedra such that a certain primitive decision problem can be written as an LP on each of those. Then the problem can be solved by a combination of enumeration and linear programming. In the second part, we analyze more specifically an instance of this problem, namely the price regulation problem that the EU encounters. Using customer-data from a large telephone operator, we compare different price regulative policies with respect to their social welfare. On the basis of the specific social welfare function that we use, we observe that other price regulative policies or different ceilings can improve the total social welfare.

We consider a revenue maximization problem where we are selling a set of items, each available in a certain quantity, to a set of bidders. Each bidder is interested in one or several bundles of items. We assume the bidders' valuations for each of these bundles to be known. Whenever bundle prices are determined by the sum of single item prices, this algorithmic problem was recently shown to be inapproximable to within a semi-logarithmic factor. We consider two scenarios for determining bundle prices that allow to break this inapproximability barrier. Both scenarios are motivated by problems where items are different, yet comparable. First, we consider classical single item prices with an additional monotonicity constraint, enforcing that larger bundles are at least as expensive as smaller ones. We show that the problem remains strongly NP-hard, and we derive a PTAS. Second, motivated by real-life cases, we introduce the notion of affine price functions, and derive fixed-parameter polynomial time algorithms.

Motivated by Ajtai's worst-case to average-case reduction for lattice problems, we study the complexity of computing short linearly independent vectors (short basis) in a lattice. We show that approximating the length of a shortest set of linearly independent vectors (shortest basis) within any constant factor is NP-hard. Under the assumption that problems in NP cannot be solved in DTIME(n p"'y'og(n)) we show that no polynomial time algorithm can approximate the length of a shortest set of linearly independent vectors (shortest basis) within a factor of 2'"g'-'("), E > 0 arbitrary, but fixed. Finally, we obtain results on the limits of non-approximability for computing short linearly independent vectors (short basis). Our strongest result in this direction states that under reasonable complexity-theoretic assumptions, approximating the length of a shortest set of linearly independent vectors (shortest basis) within a factor of n/a is not NP-hard.

We present a decomposition strategy for c-nets, i. e., rooted 3-connected planar maps. The decomposition yields an algebraic equation for the number of c-nets with a given number of vertices and a given size of the outer face. The decomposition also leads to a deterministic and polynomial time algorithm to sample c-nets uniformly at random. Using rejection sampling, we can also sample isomorphism types of convex polyhedra, i. e., 3-connected planar graphs, uniformly at random. Résumé. Nous proposons une stratégie de décomposition pour les cartes pointées 3connexes (c-réseaux). Cette décomposition permet d'obtenir une équation algébrique pour le nombre de c-réseaux suivant le nombre de sommets et la taille de la face extèrieure. On en déduit un algorithme de complexité en temps polynomiale pour le tirage aléatoire uniforme des c-réseaux. En utilisant une méthode à rejet, nous obtenons aussi un algorithme de tirage aléatoire uniforme pour les graphes planaires 3-connexes. * This is the author's version of the work. It is posted here for your personal use but not for redistribution. The definitive version was published in Proceedings of the 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC05), Séminaire Lotharingien de Combinatoire, 2006, 54A. It is available at ∼ slc/wpapers/s54Abogrjoka.pdf. 1 In the literature often the word "generating" is used instead of "sampling". We prefer "sampling" because it is more specific.

The generalized Steiner tree problem is defined as follows. Given a graph with non-negative weights and a set of pairs of vertices find the minimum network of edges such that each pair of vertices is in the same connected component. We present an algorithm for the on-line Generalized Steiner Tree (GST) problem, and two other problems: Rectilinear Steiner Arborescence(RSA) and Symmetric Rectilinear Steiner Arborescence (SRSA). For each of these problems we provide polynomial time algorithms with performance ratios of O(log n). The constant factors hidden in the O-notation are small, in the case of the GST, we are within factor 2 from the proven lower bound. The previous best on-line GST algorithm (Awerbuch et at ) was 0(log2 n)

We present fast new algorithms for phylogenetic reconstruction from distance data or weighted quartets. The methods are conservative-they will only return edges that are well supported by the input data. This approach is not only philosophically attractive; the conservative tree estimate can be used as a basis for further tree refinement or divide and conquer algorithms. The capability to process quartet data allows these algorithms to be used in tandem with ordinal or qualitative phylogenetic analysis methods. We provide algorithms for three standard conservative phylogenetic constructions: the Buneman tree, the Refined Buneman tree, and split decomposition. We introduce and exploit combinatorial formalisms involving trees, quartets, and splits, and make particular use of an attractive duality between unrooted trees, splits, and dissimilarities on one hand, and rooted trees, clusters, and similarity measures on the other. Using these techniques, we achieve O(n) improvements in the time complexity of the best previously published algorithms (where n is the number of studied species). Our algorithms will be included in the next edition of the popular Splitslkee software package.

We present a polynomial time algorithm for computing the refined Buneman tree, thereby making it applicable for tree reconstruction on large data sets. The refined Buneman tree retains many of the desirable properties of its predecessor, the well known Buneman tree, but has the practical advantage that it is typically more refined.

Entity annotation is emerging as a key enabling requirement for search based on deeper semantics: for example, a search on 'John's address', that returns matches to all entities annotated as an address that co-occur with 'John'. A dominant paradigm adopted by rulebased named entity annotators is to annotate a document at a time. The complexity of this approach varies linearly with the number of documents and the cost for annotating each document, which could be prohibiting for large document corpora. A recently proposed alternative paradigm for rule-based entity annotation , operates on the inverted index of a document collection and achieves an order of magnitude speed-up over the document-based counterpart. In addition the index based approach permits collection level optimization of the order of index operations required for the annotation process. It is this aspect that is explored in this paper. We develop a polynomial time algorithm that, based on estimated cost, can optimally select between different logically equivalent evaluation plans for a given rule. Additionally, we prove that this problem becomes NP-hard when the optimization has to be performed over multiple rules and provide effective heuristics for handling this case. Our empirical evaluations show a speed-up factor upto 2 over the baseline system without optimizations.

Poset game, which includes some famous games. e.g., Nim and Chomp as sub-games, is an important two-player impartial combinatorial game. The rule of the game is as follows: For a given poset (partial ordered set), each player intern chooses an element and the selected element and it's descendants (elements succeeding it) are all removed from the poset. A player who choose the last element is the winner. On the complexity of poset game, although it is clearly in PSPACE, it have not known whether it is in P or NP-hard. Recently a weighted poset game, which is a generalization of poset game, have been presented and it was found that some sub-games of it can be solved in polynomial-time. The complexity of this game is also open. This paper shows that weighted poset game is PSPACE-complete even if the weights are restricted in {1, -1}, the dag, which represents the poset, is bipartite, and the length of each path in the dag is at most two.

We introduce an algorithm for cooperative planning in multi-agent systems. The algorithm enables the agents to combine (fuse) their plans in order to increase their joint profits. A computational resources and skills framework is developed for representing the planned activities of an agent under time constraints. Using this resource-skill framework, we present an efficient (polynomial time) algorithm that fuses the plans of a group of agents in such a way that their joint profits improve. The framework and the algorithm are illustrated ...

We givea straightforward definition for redundancy in individual nested relations and define a new normal form that precisely characterizes redundancy for nested relations. We base our definition of redundancy on an arbitrary set of functional and multivalued dependencies, and show that our definition of nested normal form generalizes standard relational normalization theory. In addition, we give a condition that can prevent an unwanted structural anomaly in nested relations, namely, embedded nested relations with at most one tuple, Like other normal forms, our nested normal form can serve as a guide for database design.

Given a planar graph on n nodes with costs weights on its edges, de ne the distance between nodes i and j as the length of the shortest path between i and j. Consider this as an instance of metric TSP. F or any " 0, our algorithm nds a salesman tour of total cost at most 1 + " times optimal in time n O1=" 2 . We also present a quasi-polynomial time algorithm for the Steiner version of this problem.

Given a planar Rraph on n nodes with costs (weights) on its edges,-define; he distance between nodes i &d 2 as' the length of the shortest path between i and i. Consider this as &I instance of me& TSP. For any E> 6, our algorithm finds a salesman tour of total cost at most (1+ E) times optimal in time n”(llea).

Given a planar Rraph on n nodes with costs (weights) on its edges,-define; he distance between nodes i &d 2 as' the length of the shortest path between i and i. Consider this as &I instance of me& TSP. For any E> 6, our algorithm finds a salesman tour of total cost at most (1+ E) times optimal in time n”(llea).

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large N , and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Given a graph and a root, the Maximum Bounded Rooted-Tree Packing (MBRTP) problem aims at finding K rooted-trees that span the largest subset of vertices, when each vertex has a limited outdegree. This problem is motivated by peerto-peer streaming overlays in under-provisioned systems. We prove that the MBRTP problem is NP-complete. We present two polynomial-time algorithms that computes an optimal solution on complete graphs and trees respectively.

The Eulerian closed walk problem in a digraph is a well-known polynomial-time solvable problem. In this paper, we show that if we impose the feasible solutions to fulfill some precedence constraints specified by paths of the digraph, then the problem becomes NP-complete. We also present a polynomial-time algorithm to solve this variant of the Eulerian closed walk problem when the paths are arcdisjoint. We also give necessary and sufficient conditions for the existence of feasible solutions in this polynomial-time solvable case.

We present a new algorithm to canonize molecular graphs using the signature molecular descriptor introduced in the previous papers of this series. While developed specifically for molecular structures, the algorithm can be used for any graph and is not limited to acyclic graphs, planar graphs, bounded valence, or bounded genus graphs, for which polynomial time algorithms exist. The algorithm is tested with benzenoid hydrocarbons and a database of 126 705 organic compounds. The algorithm's performances are compared against Brendan Mc Kay's Nauty algorithm, which is believed to be the fastest graph canonization algorithm for general graphs, with five series of graphs each comprising up to 30 000 vertices: 2D meshes (pericondensed benzenoids), 3D cages (fullerenes and nanotubes), 3D meshes (crystal lattices), 4D cages, and power law graphs (protein and gene networks). The algorithm can be downloaded as an open source code at http://www.cs.sandia.gov/∼jfaulon/QSAR.

The first polynomial time algorithm (O(n 4)) for modular decomposition appeared in 1972 [8] and since then there have been incremental improvements, eventually resulting in linear time algorithms [22, 7, 23, 9]. Although an optimal time complexity these algorithms are quite complicated and difficult to implement. In this paper we present an easily implementable linear time algorithm for modular decomposition. This algorithm use the notion of factorizing permutation and a new datastructure, the Ordered Chain Partitions.

We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and 2−structures. We show that, under some axioms, a unique decomposition tree exists for umodules. Polynomial-time algorithms are provided for: non-trivial umodule test, maximal umodule computation, and decomposition tree computation when the tree exists. Our results unify many known decomposition like modular and bi-join decomposition of graphs, and a new decomposition of tournaments.

The longest path problem is the problem of finding a path of maximum length in a graph. As a generalization of the Hamiltonian path problem, it is NP-complete on general graphs and, in fact, on every class of graphs that the Hamiltonian path problem is NP-complete. Polynomial solutions for the longest path problem have recently been proposed for weighted trees, ptolemaic graphs, bipartite permutation graphs, interval graphs, and some small classes of graphs. Although the Hamiltonian path problem on cocomparability graphs was proved to be polynomial almost two decades ago, the complexity status of the longest path problem on cocomparability graphs has remained open until now; actually, the complexity status of the problem has remained open even on the smaller class of permutation graphs. In this paper, we present a polynomial-time algorithm for solving the longest path problem on the class of cocomparability graphs. Our result resolves the open question for the complexity of the problem on such graphs, and since cocomparability graphs form a superclass of both interval and permutation graphs, extends the polynomial solution of the longest path problem on interval graphs and provides polynomial solution to the class of permutation graphs.

We show that several classes of tree patterns observe the independence of containing patterns property, that is, if a pattern is contained in the union of several patterns, then it is contained in one of them. We apply this property to two related problems on tree pattern rewriting using views. First, given view V and query Q, is it possible for Q to have an equivalent rewriting using V which is the union of two or more tree patterns, but not an equivalent rewriting which is a single pattern? This problem is of both theoretical and practical importance because, if the answer is no, then, to find an equivalent rewriting of a tree pattern using a view, we should use more efficient methods, such as the polynomial time algorithm of [20], rather than try to find the union of all contained rewritings (which takes exponential time in the worst case) and test its equivalence to Q. Second, given a set S of views, we want to know under what conditions a subset S ′ of S is redundant in the sense that for any query Q, the contained rewritings of Q using the views in S ′ are contained in those using the views in S − S ′. Solving this problem can help us to, for example, choose the minimum number of views to be cached, or better design the virtual schema in a mediated data integration system, or avoid repeated calculation in query optimization. For the first problem, we identify several classes of tree patterns for which the equivalent rewriting can be expressed as a single tree pattern. For the second problem, we present necessary and sufficient conditions for S ′ to be redundant with respect to some classes of tree patterns. For both problems we consider extension to cases where there are rewritings using the intersection of multiple views and/or where a schema graph is present.

We study the so-called Generalized Median graph problem where the task is to to construct a prototype (i.e., a 'model') from an input set of graphs. The problem finds applications in many vision (e.g., object recognition) and learning problems where graphs are increasingly being adopted as a representation tool. Existing techniques for this problem are evolutionary search based; in this paper, we propose a polynomial time algorithm based on a linear programming formulation. We present an additional bi-level method to obtain solutions arbitrarily close to the optimal in non-polynomial time (in worst case). Within this new framework, one can optimize edit distance functions that capture similarity by considering vertex labels as well as the graph structure simultaneously. In context of our motivating application, we discuss experiments on molecular image analysis problems -the methods will provide the basis for building a topological map of all pairs of the human chromosome.

In this paper a one-machine scheduling model is analysed where n di erent jobs are classi ed into K groups depending on which additional resource they require. The change-over time from one job to another consists of the removal or the set-up time of the two jobs and is sequence-dependent in the sense that the change-over time is determined by whether or not the two jobs belong to the same group. The objective is to minimize the makespan. The problem can also be modeled as an asymmetric Traveling Salesman Problem with a special structure on the distance matrix. For this problem we give an exact solution algorithm that requires O(n 2 ) elementary operations.

Query substitution is an important problem in information retrieval. Much work focuses on how to find substitutes for any given query. In this paper, we study how to efficiently process a keyword query whose substitutes are defined by a given taxonomy. This problem is challenging because each term in a query can have a large number of substitutes, and the original query can be rewritten into any of their combinations. We propose to build an additional index (besides inverted index) to efficiently process queries. For a query workload, we formulate an optimization problem which chooses the additional index structure, aiming at minimizing the query evaluation cost, under given index space constraints. We show the NP-hardness of the problem, and propose a pseudo-polynomial time algorithm using dynamic programming, as well as an 1 4 (1 -1/e)-approximation algorithm to solve the problem. Experimental results show that, with only 10% additional index space, our approach can greatly reduce the query evaluation cost.

People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

We present a linear-time algorithm for solving the simultaneous embedding problem with fixed edges (SEFE) for a planar graph and a pseudoforest (a graph with at most one cycle) by reducing it to the following embedding problem: Given a planar graph G, a cycle C of G, and a partitioning of the remaining vertices of G, does there exist a planar embedding in which the induced subgraph on each vertex partite of G \ C is contained entirely inside or outside C? For the latter problem, we present an algorithm that is based on SPQR-trees and has linear running time. We also show how we can employ SPQR-trees to decide SEFE for two planar graphs where one graph has at most two cycles and the intersection is a pseudoforest in linear time. These results give rise to our hope that our SPQR-tree approach might eventually lead to a polynomial-time algorithm for deciding the general SEFE problem for two planar graphs. Partially supported by the German Science Foundation (JU204/11-1).

A clustered graph C = (G, T) consists of an undirected graph G and a rooted tree T in which the leaves of T correspond to the vertices of G = (V, E). Each vertex µ in T corresponds to a subset of the vertices of the graph called "cluster". c-planarity is a natural extension of graph planarity for clustered graphs, and plays an important role in automatic graph drawing. The complexity status of c-planarity testing is unknown. It has been shown in [FCE95,Dah98] that c-planarity can be tested in linear time for c-connected graphs, i.e., graphs in which the cluster induced subgraphs are connected. In this paper, we provide a polynomial time algorithm for c-planarity testing of "almost" c-connected clustered graphs, i.e., graphs for which all nodes corresponding to the non-c-connected clusters lie on the same path in T starting at the root of T , or graphs in which for each nonconnected cluster its super-cluster and all its siblings in T are connected. The algorithm is based on the concepts for the subgraph induced planar connectivity augmentation problem presented in [GJL + 02]. We regard it as a first step towards general c-planarity testing. † Partially supported by the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT).

Given a digraph G and a su ciently long directed path P, a folklore result says that G is homomorphic to P if and only if all cycles in G are balanced (the same number of forward and backward arcs). The purpose of this paper is to study homomorphisms of digraphs G that contain unbalanced cycles. In this case, we may be able to ÿnd a homomorphism of G to a power of P. Our main result states that the minimum power of P to which G admits a homomorphism equals the maximum imbalance (ratio of forward and backward arcs) of any cycle in G. The proof also yields a polynomial time algorithm to ÿnd this minimum power of P. We identify a larger class of digraphs H for which this minimum power problem can be solved in polynomial time, it includes all oriented paths H. By relating our powers of paths to complete graphs and so-called circular graphs, we are able to deduce a classical result of Minty regarding the chromatic number, as well as its more recent extension, by Goddyn, Tarsi, and Zhang, to the circular chromatic number.

Starting in 2007, the MFO publishes a preprint series which mainly contains research results related to a longer stay in Oberwolfach. In particular, this concerns the Research in Pairs-Programme (RiP) and the Oberwolfach-Leibniz-Fellows (OWLF), but this can also include an Oberwolfach Lecture, for example. A preprint can have a size from 1-200 pages, and the MFO will publish it on its website as well as by hard copy. Every RiP group or Oberwolfach-Leibniz-Fellow may receive on request 30 free hard copies (DIN A4, black and white copy) by surface mail. Of course, the full copy right is left to the authors. The MFO only needs the right to publish it on its website www.mfo.de as a documentation of the research work done at the MFO, which you are accepting by sending us your file. In case of interest, please send a pdf file of your preprint by email to or , respectively. The file should be sent to the MFO within 12 months after your stay as RiP or OWLF at the MFO. ri e ow e p There are no requirements for the format of the preprint, except that the introduction should contain a short appreciation and that the paper size (respectively format) should be DIN A4, "letter" or "article". On the front page of the hard copies, which contains the logo of the MFO, title and authors, we shall add a running number (20XX-XX). We cordially invite the researchers within the RiP or OWLF programme to make use of this offer and would like to thank you in advance for your cooperation.

We present a new algebraic algorithmic scheme to solve convex integer maximization problems of the following form, where c is a convex function on R d and w 1 x,. .. , w d x are linear forms on R n , max {c(w 1 x,. .. , w d x) : Ax = b, x ∈ N n }. This method works for arbitrary input data A, b, d, w 1 ,. .. , w d , c. Moreover, for fixed d and several important classes of programs in variable dimension, we prove that our algorithm runs in polynomial time. As a consequence, we obtain polynomial time algorithms for various types of multi-way transportation problems, packing problems, and partitioning problems in variable dimension.

We provide a polynomial time algorithm for computing the universal Gröbner basis of any polynomial ideal having a finite set of common zeros in fixed number of variables. One ingredient of our algorithm is an effective construction of the state polyhedron of any member of the Hilbert scheme Hilb d n of n-long d-variate ideals, enabled by introducing the Hilbert zonotope H d n and showing that it simultaneously refines all state polyhedra of ideals on Hilb d n .

In this article we study a broad class of integer programming problems in variable dimension. We show that these so-termed n-fold integer programming problems are polynomial time solvable. Our proof involves two heavy ingredients discovered recently: the equivalence of linear optimization and so-called directed augmentation, and the stabilization of certain Graver bases. We discuss several applications of our algorithm to multiway transportation problems and to packing problems. One important consequence of our results is a polynomial time algorithm for the d-dimensional integer transportation problem for long multiway tables. Another interesting application is a new algorithm for the classical cutting stock problem.