A feedback vertex set of a graph is a subset of vertices that contains at least one vertex from every cycle in the graph. The problem considered is that of finding a minimum feedback vertex set given a weighted and undirected graph. We present a…
Papers in Discrete Mathematics
Discrete Mathematics papers in Mathematics, A
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In the k-level uncapacitated facility location problem, we have a set of demand points where clients are located. The demand of each client is known. Facilities have to be located at given sites in order to service the clients, and each client is to…
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Until now, the analysis of fault tolerance of peer-to-peer systems usually only covers random faults of some kind. Contrary to traditional algorithmic research, faults as well as joins and leaves occurring in a worst-case manner are hardly…
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We propose a way of measuring the similarity of a Boolean vector to a given set of Boolean vectors, motivated in part by certain data mining or machine learning problems. We relate the similarity measure to one based on Hamming distance and we…
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Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a…
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This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question posed in 1981 by Grötschel, Lovász, and Schrijver. The algorithm employs a scaling scheme that uses a flow in the complete…
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"A Companion to Phenomenology and Existentialism is a complete guide to two of the dominant movements of philosophy in the twentieth century. Written by a team of leading scholars, including Dagfinn Føllesdal, J. N. Mohanty, Robert Solomon, Jean-Luc…
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The range of Fourier methods can be significantly increased by extending a nonperiodic function f(x) to a periodic function height=''18`` width=''12``> on a larger interval. When f(x) is analytically known on the extended interval, the extension is…
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Logistic regression is a workhorse of statistics and is closely related to methods used in Machine Learning, including the Perceptron and the Support Vector Machine. This note compares eight different algorithms for computing the maximum…
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There are many (mixed) integer programming formulations of the Steiner problem in networks. The corresponding linear programming relaxations are of great interest particularly, but not exclusively, for computing lower bounds; but not much has been…
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In 1997-1998, the Netherlands experienced a large epidemic of classical swine fever (CSF). The magnitude of this epidemic stressed the role information systems could play in supporting the management during an eradication campaign. The enforcement…
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Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book…
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In this note we put forward a conjecture on the average optimal length for bipartite matching with a finite number of elements where the different lengths are independent one from the others and have an exponential distribution.
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The screening of data sets for "positive data objects" is essential to modern technology. A (group) test that indicates whether a positive data object is in a specific subset or pool of the dataset can greatly facilitate the identification of all…
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We present a counterexample contradicting the equivalence of statements (i)-(ii) and (iii)-(v) of Theorem 1 of Fu, Chen, and Niculescu (2006). (C) 2009 Elsevier Ltd. All rights reserved.
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Gouvea and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this note, we exhibit explicit examples contradicting the full conjecture as it currently stands.
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A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were rst introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in…
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A fast multilevel wavelet collocation method for the solution of partial differential equations in multiple dimensions is developed. The computational cost of the algorithm is independent of the dimensionality of the problem and is O(), where is the…
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Theclassical maximum flow problem sometimes occurs in settings in whichthe arc capacities are not fixed but are functions ofa single parameter, and the goal is to find thevalue of the parameter such that the corresponding maximum flowor minimum cut…
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We present a direct solver for the Poisson and Laplace equations in a 3D rectangular box. The method is based on the application of the discrete Fourier transform accompanied by a subtraction technique which allows reducing the errors associated…
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