Randomized Algorithms

This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. The authors solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less conservative than the existing one. The new sampling strategy enables the definition of efficient hierarchical sample reuse algorithms that reduce significantly the computational complexity and make it independent of the dimension of the uncertainty space. Moreover, the authors show that there exists a one to one correspondence between the new and the existing robustness measures and provide a computationally simple algorithm to derive one from the other.

The Euclidean Minimum Spanning Tree problem is to decide whether a given graph G = ( P, E) on a set of points in the two dimensional plane is a minimum spanning tree with respectto the Euclidean distance. Czumaj, Sohler, and Ziegler [2] gave a 1-sided-error non-adaptive property-tester for this task of query complexity eO(pn). We show that every non-adaptive (notnecessarily 1-sided-error) property-tester for this task has a query complexity of \Omega (p n), implyingthat the test in [2] is of best complexity. We further prove that every adaptive property-tester

We propose an improved private count-mean-sketch data structure and show its applicability to differentially private contact tracing. Our proposed scheme (Diversifed Averaging for Meta estimation of Sketches-DAMS) provides a better trade-off between true positive rates and false positive rates while maintaining differential privacy (a widely accepted formal standard for privacy). We show its relevance to the social good application of private digital contact tracing for COVID-19 and beyond. The scheme involves one way locally differentially private uploads from the infected client devices to a server that upon a postprocessing obtains a private aggregated histogram of locations traversed by all the infected clients within a time period of interest. The private aggregated histogram is then downloaded by any querying client in order to compare it with its own data on-device, to determine whether it has come into close proximity of any infected client or not. We present empirical exper...

The goal of approximating metric spaces by more simple metric spaces has led to the notion ofgraph spanners [PU89, PS891 and to low-distortion embeddings in low-dimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for ...

This short note is about the assertion in AIMA(Russell and Norvig, 2010, p.221) that " on the n-queens problem, if you don't count the initial placement of queens, the run time of min-conflicts is roughly independent of problem size ". We learnt the hard way, that to verify this statement , we need to carefully implement the heuristic with full rigour.

Unfair metrical task systems are a generalization of online metrical task systems. In this paper we introduce new techniques to combine algorithms for unfair metrical task systems and apply these techniques to obtain improved randomized online algorithms for metrical task systems on arbitrary metric spaces.

The vehicle routing problem (VRP) is a flourishing research area with clear applications to real-life distribution companies. However, most VRP-related academic articles assume the existence of a homogeneous fleet of vehicles and/or a symmetric cost matrix. These assumptions are not always reasonable in real-life scenarios. To contribute in closing this gap between theory and practice, we propose a hybrid methodology for solving the asymmetric and heterogeneous vehicle routing problem (AHVRP). In our approach, we consider: 1) different types of vehicle loading capacities (heterogeneous fleets); 2) asymmetric distance-based costs. The proposed approach combines a randomised version of a well-known savings heuristic with several local searches specifically adapted to deal with the asymmetric nature of costs. A computational experiment allows us to discuss the efficiency of our approach and also to analyse how routing costs vary when slight departures from the homogeneous fleet assumption are considered.

In our information societies, we increasingly delegate tasks and decisions to automated systems, devices and agents that mediate human relationships, by taking decisions and acting on the basis of algorithms. Their increased intelligence, autonomous behavior and connectivity are changing crucially the life conditions of human beings as well as altering traditional concepts and ways of understanding reality. Algorithms are directed to solve problems that are not always detectable in their own relevance and timeliness. They are also meant to solve those problems through procedures that are not always visible and assessable in their own. In addition, technologies based on algorithmic procedures more and more infer personal information from aggregated data, thus profiling human beings and anticipating their expectations, views and behaviors. This may have normative, if not discriminatory, consequences. While algorithmic procedures and applications are meant to serve human needs, they risk to create an environment in which human beings tend to develop adaptive strategies by conforming their behaviour to the expected output of the procedures, with serious distortive effects. Against this backdrop, little room is often left for a process of rational argumentation able to challenge the results of algorithmic procedures by putting into question some of their hidden assumptions or by taking into account some neglected aspects of the problems under consideration. At the same time, it is widely recognized that scientific and social advances crucially depend on such an open and free critical discussion.

We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their internal structures, and allows for introducing modifications, as illustrated with SVD, QR, and UTV factorizations. The prospect of meta-factorization also provides insights into computational aspects of generalized matrix inverses and randomized linear algebra algorithms. The relations between the Moore-Penrose pseudoinverse, generalized Nyström method, and the CUR decomposition are revealed here as an illustration. Finally, meta-factorization offers hints on the structure of new factorizations and provides the potential of creating them.

Randomized Algorithms are now gaining the attention of
researchers. The reason is that some of the randomized
algorithms have been successfully implemented in important
applications reducing the time complexity and other
computing resources. This paper reviews the different
methods and techniques available in randomized algorithms.
Paper also gives the gaps in the existing research and the
future scope of research in this area.

We describe an alternative to gradient descent for backpropogation through a neural network, which we call Blind Descent. We believe that Blind Descent can be used to augment backpropagation by using it as an initialisation method and can also be used at saturation. Blind Descent, inherently by design, does not face problems like exploding or vanishing gradients.

—This paper contributes to the development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed SC networks (SCNs). In contrast to the existing randomized learning algorithms for single layer feed-forward networks, we randomly assign the input weights and biases of the hidden nodes in the light of a supervisory mechanism, and the output weights are analytically evaluated in either a constructive or selective manner. As fundamentals of SCN-based data modeling techniques, we establish some theoretical results on the universal approximation property. Three versions of SC algorithms are presented for data regression and classification problems in this paper. Simulation results concerning both data regression and classification indicate some remarkable merits of our proposed SCNs in terms of less human intervention on the network size setting, the scope adaptation of random parameters, fast learning, and sound generalization.

In this article we provide an introduction to data structures and algorithms. We consider some basic data structures and deal with implementations of a dictionary and a priority queue. Algorithms for such basic problems as matrix multiplication, binary search, sorting, and selection are given. The concepts of randomized computing and parallel computing are also visited.

Hyperspectral imaging techniques such as matrix-assisted laser desorption ionization (MALDI) mass spectrometry imaging produce large, information-rich datasets that are frequently too large to be analyzed as a whole. In addition, the "curse of dimensionality" adds fundamental limits to what can be done with such data, regardless of the resources available. We propose and evaluate random matrix-based methods for the analysis of such data, in this case, a MALDI mass spectrometry image from a section of rat brain. By constructing a randomized orthornormal basis for the data, we are able to achieve reductions in dimensionality and data size of over 100 times. Furthermore, this compression is reversible to within noise limits. This allows more-conventional multivariate analysis techniques such as principal component analysis (PCA) and clustering methods to be directly applied to the compressed data such that the results can easily be back-projected and interpreted in the original measurement space. PCA on the compressed data is shown to be nearly identical to the same analysis on the original data but the run time was reduced from over an hour to 8 seconds. We also demonstrate the generality of the method to other data sets, namely, a hyperspectral optical image of leaves, and a Raman spectroscopy image of an artificial ligament. In order to allow for the full evaluation of these methods on a wide range of data, we have made all software and sample data freely available.

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We consider a model with n players and m objects. Each player has a “preference vector ” of length m that models his grade for each object. The grades are unknown to the players. A player can learn his grade for an object by probing that object, but performing a probe incurs cost. The goal of a player is to learn his preference vector with minimal cost, by adopting the results of probes performed by other players. To facilitate communication, we assume that players collaborate by posting their grades for objects on a shared billboard: reading from the billboard is free. We consider players whose preference vectors are popular, i.e., players whose preferences are common to many other players. We present distributed and sequential algorithms to solve the problem with logarithmic cost overhead. Categories and Subject Descriptors

We consider a model with n players and m objects. Each player has a “preference vector ” of length m that models his grade for each object. The grades are unknown to the players. A player can learn his grade for an object by probing that object, but performing a probe incurs cost. The goal of a player is to learn his preference vector with minimal cost, by adopting the results of probes performed by other players. To facilitate communication, we assume that players collaborate by posting their grades for objects on a shared billboard: reading from the billboard is free. We consider players whose preference vectors are popular, i.e., players whose preferences are common to many other players. We present distributed and sequential algorithms to solve the problem with logarithmic cost overhead.

Unfair metrical task systems are a generalization of online metrical task systems. In this paper we introduce new techniques to combine algorithms for unfair metrical task systems and apply these techniques to obtain improved randomized online algorithms for metrical task systems on arbitrary metric spaces.

Fragmentin è un collettivo artistico fondato nel 2014 a Losanna. È formato da Marc Dubois (1985), David Colombini (1989) e Laura Perrenoud (1991): tre Alumni della ECAL (Lausanne University of Art and Design) le cui opere testimoniano una ricerca che intreccia ricerca formale e competenze di ingegneria, linguaggio scultoreo e conoscenza digitale: lavori che oltrepassano la dimensione estetica per stimolare discussioni critiche su alcuni temi della contemporaneità. Tra questi spicca il rapporto tra tecnologia digitale e vita quotidiana, cruciale nel momento in cui la logica predittiva degli algoritmi influenza le scelte e i gusti personali, eliminando gradualmente ogni casualità dalla quotidiana esplorazione del mondo. L'attivista Eli Pariser ha chiamato questo fenomeno 'Bolla di Filtraggio' nel suo testo "The Filter Bubble: What The Internet Is Hiding From You" pubblicato nel 2012 da Penguin Books. Come ricreare, quindi, dei margini di randomness in un sistema sempre più recintato da codici di informazione che prevedono il futuro come delle infallibili sibille contemporanee?

We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the cycle space identifies the cuts of a graph. This leads to simple new linear-time sequential algorithms for finding all cut edges and cut pairs (a set of 2 edges that form a cut) of a graph.

We present a cooperative framework for content-based image retrieval for the realistic setting where images are distributed across multiple cooperating servers. The proposed method is in line with bag-of-features approaches but uses fully data-independent, randomized structures, shared by the cooperating servers, to map image features to common visual words. A coherent, global image similarity measure (which is a kernel) is computed in a distributed fashion over visual words, by only requiring a small amount of data transfers between nodes. Our experiments on various image types show that this framework is a very promising step towards large-scale, distributed content-based image retrieval.

"El proceso de estimación de una proporción relacionada con una pregunta que puede ser altamente sensible para el encuestado, puede generar respuestas que no necesariamente coinciden con la realidad. Para reducir la probabilidad de respuestas falsas a este tipo de preguntas algunos autores han propuesto técnicas de respuesta aleatorizada asumiendo un error de observación asimétrico. En este artículo se presenta una generalización al caso donde se asume un error simétrico lo cual puede ser un supuesto poco realista en la práctica. Se deduce la función de verosimilitud bajo el supuesto de error de estimación asimétrico.

Con esto se pretende que en la práctica se cuente con un método alternativo para reducir la probabilidad de respuestas falsas. Asumiendo distribuciones a priori informativas se encuentra una expresión para la distribución posterior. Puesto que esta última no tiene una expresión cerrada es necesario usar el muestreador de Gibbs en el proceso de estimación. Esta técnica se ilustra usando datos reales sobre consumo de drogas recolectados por la Oficina de Bienestar de la Universidad Nacional de Colombia, Sede Medellín"

Urban transportation is a strategic domain that has become an important issue for client satisfaction in distribution companies. In academic literature, this problem is categorized as a Vehicle Routing Problem, a popular research stream that has undergone significant theoretical advances but has remained far from practice implementations. Most Vehicle Routing Problems usually assume homogenous fleets, that is, all vehicles are considered of the same type and size. In reality, this is usually not the case as most companies use different types of trucks to distribute their products. Also, researchers consider symmetric distances between customers. However, in intra-urban distribution it is more appropriate to consider asymmetric costs. In this study, we address the Heterogeneous Fixed Fleet Vehicle Routing Problem with some additional constraints: (a) Asymmetric Cost matrix, (b) Service Times and (c) Routes Length restrictions. Our objective function is to reduce the total routing costs. We present an approach using a multi-start algorithm that combines a randomized Clarke & Wright's Savings heuristic and a local search procedure. We execute our algorithm with data from a company that distributes food to more than 50 customers in Barcelona. The results reveal promising improvements when compared to an approximation of the company's route planning.

See is an abstract machine for computation programmed in the 3 word, syntax free language #Logica.  It is thought to be Turing complete and is a language designed to be used with the 4th word 'meta'. The definition of meta can be found here: http://github.com/BusFactor1Inc/explain.

This is the source code and commentary for the first Saphion emulator (and test harness), 'expect', part of the 'explain' package.  It is a game of proof and indecision and thought and language.  It is a new form of communication with the machine.  And people.

Virtual private network design is the following NP-hard problem. We are given a communication network represented as a weighted graph with thresholds on the nodes which represent the amount of flow that a node can send to and receive from the network. The task is to reserve capacities at minimum cost and to specify paths between every ordered pair of nodes such that all valid traffic-matrices can be routed along the corresponding paths. Recently, this network design problem has received considerable attention in the literature. It is motivated by the fact that the exact amount of flow which is exchanged between terminals is not known in advance and prediction is often elusive. The main contributions of this paper are as follows: (1) Using Hu's 2-commodity flow theorem, we provide a new and considerably stronger lower bound on the cost of an optimum solution. With this lower bound we reanalyze a simple routing scheme which has been described in the literature many times, and provide an improved upper bound on its approximation ratio. We present a new randomized approximation algorithm. In contrast to earlier approaches from the literature, the resulting solution does not have tree structure. A combination of our new algorithm with the simple routing scheme yields an expected performance ratio of 3.79 for virtual private network design. This is a considerable improvement of the previously best known 5.55-approximation result [A. Gupta, A. Kumar, and T. Roughgarden, Simpler and better approximation algorithms for network design, in Proceedings of the ACM Symposium on Theory of Computing, ACM, New York, 2003, pp. 365-372]. Our VPND algorithm uses a Steiner tree approximation algorithm as a subroutine. It is known that an optimum Steiner tree can be computed in polynomial time if the number of terminals is logarithmic. Replacing the approximate Steiner tree computation with an exact one whenever the number of terminals is sufficiently small, we finally reduce the approximation ratio to 3.55. To the best of our knowledge, this is the first time that a nontrivial result from exact (exponential) algorithms leads to an improved polynomial-time approximation algorithm.

Rapid access to information is essential for a wide variety of retrieval systems and applications. Hashing has long been used when the fastest possible direct search is desired, but is generally not appropriate when sequential or range searches are also required. This paper describes a hashing method, developed for collections that are relatively static, that supports both direct and sequential access. Indeed, the algorithm described gives hash functions that are optimal in terms of time and hash table space utilization, and that preserve any a priori ordering desired. Furthermore, the resulting order preserving minimal perfect hash functions (OPMPHFs) can be found using space and time that is on average linear in the number of keys involved.

El hombre siempre se ha visto afectado por la aleatoriedad de algunos fenómenos y ha sentido la necesidad de generarla para diversos experimentos científicos, tanto en el mundo de las matemáticas como en el de las ciencias de la computación, hoy ligadas más que nunca a los nuevos paradigmas educativos.
El auge que están experimentando los cursos masivos online (MOOC) en los últimos años, está haciendo que cada vez sea más necesario analizar la fiabilidad de los test de evaluación que aparecen en las distintas plataformas de aprendizaje online. No solamente en cuanto al funcionamiento de estas plataformas, sino también para equilibrar las preguntas y respuestas de los exámenes tipo test. No debe olvidarse que ante un curso con miles de estudiantes de todo el mundo, algunos de ellos tratarán de hacer trampas para obtener los mejores resultados en el menor tiempo posible.

We consider the problem of electing a leader among nodes in a highly dynamic network where the adversary has unbounded capacity to insert and remove nodes (including the leader) from the network and change connectivity at will. We present a randomized algorithm that (re)elects a leader in O(D log n) rounds with high probability, where D is a bound on the dynamic diameter of the network and n is the maximum number of nodes in the network at any point in time. We assume a model of broadcast-based communication where a node can send only 1 message of O(log n) bits per round and is not aware of the receivers in advance. Thus, our results also apply to mobile wireless adhoc networks, improving over the optimal (for deterministic algorithms) O(Dn) solution presented at FOMC 2011. We show that our algorithm is optimal by proving that any randomized Las Vegas algorithm takes at least Ω(D log n) rounds to elect a leader with high probability, which shows that our algorithm yields the best possible (up to constants) termination time.

The vehicle routing problem (VRP) is a flourishing research area with clear applications to real-life distribution companies. However, most VRP-related academic articles assume the existence of a homogeneous fleet of vehicles and/or a symmetric cost matrix. These assumptions are not always reasonable in real-life scenarios. To contribute closing this gap between theory and practice, we propose a hybrid methodology for solving the asymmetric and heterogeneous vehicle routing problem (AHVRP). In our approach, we consider: 1) different types of vehicle loading capacities (heterogeneous fleets); 2) asymmetric distance-based costs. The proposed approach combines a randomised version of a well-known savings heuristic with several local searches specifically adapted to deal with the asymmetric nature of costs. A computational experiment allows us to discuss the efficiency of our approach and also to analyse how routing costs vary when slight departures from the homogeneous fleet assumption are considered.

We give an O(log 4 n)-time O(n 2)-processor CRCW PRAM algorithm to nd a hamiltonian cycle in a strong semicomplete bipartite digraph, B, provided that a factor of B (i.e. a collection of vertex disjoint cycles covering the vertex set of B) is computed in a preprocessing step. The factor is found (if it exists) using a bipartite matching algorithm, hence placing the whole algorithm in the class Random-NC. We show that any parallel algorithm which can check the existence of a hamiltonian cycle in a strong semicomplete bipartite digraph in time O(r(n)) using p(n) processors can be used to check the existence of a perfect matching in a bipartite graph in time O(r(n) + n 2 =p(n)) using p(n) processors. Hence, our problem belongs to the class NC if and only if perfect matching in bipartite graphs belongs to NC. We also consider the problem of nding a hamiltonian path in a semicomplete bipartite digraph.

Originally I am dealing with the issue of an arbitrary random number X that maybe bigger than the limit of greatest Rand() so since there are more than one Rand() with different limits then we could have break down X=L1*A+L2*B+L3*C+L4*D now just a rand(L1)*A+rand(L2)*B+rand(L3)*C+rand(L4)*D is sufficient. Then since there maybe more than one way to make up X via those Limits of random number then the output random number has an added unpredictability since one first has to predict which made-up then predict the result of which method. i.e. There could be algorithmic complexity in finding the formula of L1*A+L2*B+L3*C+L4*D (dimension 1), then that compound with yet another algorithmic complexity in doing the rand(L1/L2/L3/L4) (dimension 2). Moreover, since anything below L1/L2/L3/L4 is also the result of respective rand(), thus anything less than them is a valid component in that L1*A+L2*B+L3*C+L4*D formula, one then is not limited the number of rand() provided by the OS thus one could have L1*A+L2*B+L3*C+L4*D+L5*E+L6*F then it became rand(L1)*A+rand(L2)*B+rand(L3)*C+rand(L4)*D+rand(L5)*E+rand(L6)*F..... etc. Or using Operator Invertor program one can have a very long formula replacing  L1*A+L2*B+L3*C+L4*D+L5*E+L6*F  with additional +/-/*/...(L1*A-L2*B+L3*C-L4*D+L5*E-L6*F....etc), give the operators need that OI program would find the value to create the needed value. The next level for that program is given the total number of operators that OI program randomly decided the operators then the value, yet another level is with the inclusion of brackets (i.e. branches). Then there would be uncertainties in number of operators and complexities of the formula for that random number, let alone any part of that made formula could be randomize recursively (L1*A+L2*B+L3*C+L4*D+L5*E+L6*F, dimensions within dimensions ). I don't know if it is possible to write a program to retro created a program to make up that number in such a way, then a program to 'randomize' the complexity and various algorithmic properties and parameters. Essentially there are four levels of complexities in this random number making paradigm:
1. Total length of the formula result in the resulting random number;
2. Along with 1, the exact operators between the components for that made-up formula;
3. Along with 1, the exact parameters that acts as the components for that formula;
4. The complexity of the formula as in 1.
5/6/7. The method in randomize the values of 2/3/4.
Thus any random number of any value could be made up via any level of complexities, the unpredictabilities just added another level of complexities and unpredictableness. Now given the parameters in the program that determine 2/3/4 could also be of any complexities, and the process to create that program could be randomize. Thus we had infinite level of recursive complexity build within ANY RANDOM VALUE.

For any value of decimal number 0.abcdefghi...etc the easiest way is calculate abcdefghi... as in above then shift its value, or translated that into a form with fractions that is (L1*A+L2*B+L3*C+L4*D+L5*E)/(L2*A+L3*B+L4*C+L5*D+L5*E+L6*F),  then randomize the above and below values using aforementioned method, or bounded that value between two fractions in the like of (L1*A+L2*B+L3*C+L4*D+L5*E)/(L2*A+L3*B+L4*C+L5*D+L5*E+L6*F) and  break down the values in the form of (L1*A+L2*B+L3*C+L4*D+L5*E) with a lower limit and upper limit then do a randomization of (L1*A+L2*B+L3*C+L4*D+L5*E). Thus we arrived  at a really simple way to using the existing tools from the OS to create a random value that is unpredictable by any quantum computer or almost any algorithm.