If robots are deployed in large numbers in disaster scenarios, the ability to discover and exchange resources and services with other robots in an open, heterogeneous, large-scale network will be essential for a succe...
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Vertex deletion problems ask whether it is possible to delete at most k vertices from a graph so that the resulting graph belongs to a specified graph class. Over the past years, the parameterized complexity of vertex...
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Schematic metro maps in practice as well as metro map layout algorithms usually adhere to an octilinear layout style with all paths composed of horizontal, vertical, and 45◦-diagonal edges. Despite growing interest in...
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Hedonic diversity games are a variant of the classical hedonic games designed to better model a variety of questions concerning diversity and fairness. Previous works mainly targeted the case with two diversity classe...
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In 1959, Erdos and Gallai proved that every graph G with average vertex degree ad(G) ≥ 2 contains a cycle of length at least ad(G). We provide an algorithm that for k ≥ 0 in time 2O(k) nO(1) decides whether a 2-conn...
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Consider the balanced Ramsey game, in which a player has r colors and where in each round r random edges of an initially empty graph on n vertices are presented. The player has to immediately assign a different color ...
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Indicator-based algorithms have become a very popular approach to solve multi-objective optimization problems. In this paper, we contribute to the theoretical understanding of algorithms maximizing the hypervolume for...
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ISBN:
(纸本)9781605583259
Indicator-based algorithms have become a very popular approach to solve multi-objective optimization problems. In this paper, we contribute to the theoretical understanding of algorithms maximizing the hypervolume for a given problem by distributing μ points on the Pareto front. We examine this common approach with respect to the achieved multiplicative approximation ratio for a given multi-objective problem and relate it to a set of μ points on the Pareto front that achieves the best possible approximation ratio. For the class of linear fronts and a class of concave fronts, we prove that the hypervolume gives the best possible approximation ratio. In addition, we examine Pareto fronts of different shapes by numerical calculations and show that the approximation computed by the hypervolume may differ from the optimal approximation ratio. Copyright 2009 ACM.
For any graph F and any integer r≥2, the online vertex-Ramsey density of F and r, denoted m*(F, r), is a parameter defined via a deterministic two-player Ramsey-type game (Painter vs. Builder). This parameter was int...
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The decomposition of graphs is a prominent algorithmic task with numerous applications in computer science. A graph decomposition method is typically associated with a width parameter (such as treewidth) that indicate...
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The decomposition of graphs is a prominent algorithmic task with numerous applications in computer science. A graph decomposition method is typically associated with a width parameter (such as treewidth) that indicates how well the given graph can be decomposed. Many hard (even #P-hard) algorithmic problems can be solved efficiently if a decomposition of small width is provided;the runtime, however, typically depends exponentially on the decomposition width. Finding an optimal decomposition is itself an NP-hard task. In this paper we propose, implement, and test the first practical decomposition algorithms for the width parameters treecut width and treedepth. These two parameters have recently gained a lot of attention in the theoretical research community as they offer the algorithmic advantage over treewidth by supporting so-called fixed-parameter algorithms for certain problems that are not fixed-parameter tractable with respect to treewidth. However, the existing research has mostly been theoretical. A main obstacle for any practical or experimental use of these two width parameters is the lack of any practical or implemented algorithm for actually computing the associated decompositions. We address this obstacle by providing the first practical decomposition algorithms. Our approach for computing treecut width and treedepth decompositions is based on efficient encodings of these decomposition methods to the propositional satisfiability problem (SAT). Once an encoding is generated, any satisfiability solver can be used to find the decomposition. This allows us to leverage the surprising power of todays state-of-the art SAT solvers. The success of SAT-based decomposition methods crucially depends on the used characterisation of the decomposition method, as not every characterisation is suitable for that task. For instance, the successful leading SAT encoding for treewidth is based on a characterisation of treewidth in terms of elimination orderings. For treecut w
This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting ...
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