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Some of today’s applications run on computer platforms with large and inexpensive memories, which are also error-prone. Unfortunately, the appearance of even very few memory faults may jeopardize the correctness of the computational results. An algorithm is resilient to memory faults if, despite the corruption of some memory values before or during its execution, it is nevertheless able to get a correct...
The Metric Labeling problem is an elegant and powerful mathematical model capturing a wide range of classification problems that arise in computer vision and related fields. In a typical classification problem, one wishes to assign labels to a set of objects to optimize some measure of the quality of the labeling. The metric labeling problem captures a broad range of classification problems where...
Historically, the idea of symmetry has played a much greater role in physics than in computer science. While computer scientists typically work against an adversary, physicists are brought up to believe in the benevolence of nature, and to believe that the answers to natural questions are often as simple—and as symmetric—as they possibly could be. Indeed, symmetry is intimately linked to every branch...
We study the problem of exploring an unknown, strongly connected directed graph. Starting at some node of the graph, we must visit every edge and every node at least once. The goal is to minimize the number of edge traversals. It is known that the competitive ratio of online algorithms for this problem depends on the deficiency d of the graph, which is the minimum number of edges that must be added...
We consider the problem of routing a message in a mesh network with faulty nodes. The number and positions of faulty nodes is unknown. It is known that a flooding strategy like expanding ring search can route a message in the minimum number of steps h while it causes a traffic (i.e. the total number of messages) of ${\mathcal O}(h^{2})$ . For optimizing traffic a single-path strategy is optimal...
We propose heuristics to reduce the number of shortest path computations required to compute a 1+ε approximation to the maximum multicommodity flow in a graph. Through a series of improvements we are able to reduce the number of shortest path computations significantly. One key idea is to use the value of the best multicut encountered in the course of the algorithm. For almost all instances this multicut...
We present an evaluation of a Lagrangean-based branch-and-bound algorithm with additional valid inequalities for the capacitated network design problem. The focus is on two types of valid inequalities, the cover inequalities and local cuts. We show how these inequalities can be considered in a Lagrangean relaxation without destroying the computationally simple structure of the subproblems. We present...
We consider the price of stability for Nash and correlated equilibria of linear congestion games. The price of stability is the optimistic price of anarchy, the ratio of the cost of the best Nash or correlated equilibrium over the social optimum. We show that for the sum social cost, which corresponds to the average cost of the players, every linear congestion game has Nash and correlated price of...
We present algorithms and complexity results for the problem of finding equilibria (mixed Nash equilibria, pure Nash equilibria and correlated equilibria) in games with extremely succinct description that are defined on highly regular graphs such as the d-dimensional grid; we argue that such games are of interest in the modelling of large systems of interacting agents. We show that mixed Nash equilibria...
The best known algorithms for the computation of market equilibria, in a general setting, are not guaranteed to run in polynomial time. On the other hand, simple poly-time algorithms are available for various restricted – yet important – markets. In this paper, we experimentally explore the gray zone between the general problem and the poly-time solvable special cases. More precisely, we analyze...
Divide-and-conquer strategy based on variations of the Lipton-Tarjan planar separator theorem has been one of the most common approaches for solving planar graph problems for more than 20 years. We present a new framework for designing fast subexponential exact and parameterized algorithms on planar graphs. Our approach is based on geometric properties of planar branch decompositions obtained by Seymour...
We present an algorithm that decides the satisfiability of a CNF formula where every variable occurs at most k times in time $O(2^{N(1-c/(k+1)+O(1/k^{2}))})$ for some c (that is, O(αN) with α< 2 for every fixed k). For k ≤ 4, the results coincide with an earlier paper where we achieved running times of O(20.1736 N) for k = 3 and O(20.3472N...
For a given graph G of n vertices and m edges, a clique S of size k is said to be c-isolated if there are at most ck outgoing edges from S. It is shown that this parameter c is an interesting measure which governs the complexity of finding cliques. In particular, if c is a constant, then we can enumerate all c-isolated maximal cliques in linear time, and if c = O(log n), then we can enumerate all...
We present an algorithm for finding shortest surface non-separating cycles in graphs with given edge-lengths that are embedded on surfaces. The time complexity is O(g3/2V3/2log V + g5/2V1/2), where V is the number of vertices in the graph and g is the genus of the surface. If g = o(V1/3 − ε), this represents a...
In geographic information retrieval, queries often use names of geographic regions that do not have a well-defined boundary, such as “Southern France.” We provide two classes of algorithms for the problem of computing reasonable boundaries of such regions, based on evidence of given data points that are deemed likely to lie either inside or outside the region. Our problem formulation leads to a number...
We present the first release of the Exacus C++ libraries. We aim for systematic support of non-linear geometry in software libraries. Our goals are efficiency, correctness, completeness, clarity of the design, modularity, flexibility, and ease of use. We present the generic design and structure of the libraries, which currently compute arrangements of curves and curve segments of low algebraic degree,...
Traditionally, clustering problems are investigated under the assumption that all objects must be clustered. A shortcoming of this formulation is that a few distant objects, called outliers, may exert a disproportionately strong influence over the solution. In this work we investigate the k -min-sum clustering problem while addressing outliers in a meaningful way. Given a complete graph G =...
We present two polynomial-time approximation algorithms for the metric case of the maximum traveling salesman problem. One of them is for directed graphs and its approximation ratio is . The other is for undirected graphs and its approximation ratio is $\frac{7}{8} - o(1)$ . Both algorithms improve on the previous bests.
We introduce the Minimum-size bounded-capacity cut (MinSBCC) problem, in which we are given a graph with an identified source and seek to find a cut minimizing the number of nodes on the source side, subject to the constraint that its capacity not exceed a prescribed bound B. Besides being of interest in the study of graph cuts, this problem arises in many practical settings, such as in epidemiology,...
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