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On treewidth and related parameters of random geometric graphs *
, 2017 Dieter Mitsche, Guillem Perarnau
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2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), 2023 We present a data structure that for a dynamic graph G that is updated by edge insertions and deletions, maintains a tree decomposition of G of width at most $6 k+5$ under the promise that the treewidth of G never grows above k. The amortized update time
T. Korhonen +4 more
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Bounding twin-width for bounded-treewidth graphs, planar graphs, and bipartite graphs
International Workshop on Graph-Theoretic Concepts in Computer Science, 2022Twin-width is a newly introduced graph width parameter that aims at generalizing a wide range of"nicely structured"graph classes. In this work, we focus on obtaining good bounds on twin-width $\text{tww}(G)$ for graphs $G$ from a number of classic graph ...
Hugo Jacob, Marcin Pilipczuk
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Hedonic Games and Treewidth Revisited
Embedded Systems and Applications, 2022We revisit the complexity of the well-studied notion of Additively Separable Hedonic Games (ASHGs). Such games model a basic clustering or coalition formation scenario in which selfish agents are represented by the vertices of an edge-weighted digraph $G=
T. Hanaka, M. Lampis
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Edge-Cut Width: An Algorithmically Driven Analogue of Treewidth Based on Edge Cuts
International Workshop on Graph-Theoretic Concepts in Computer Science, 2022Decompositional parameters such as treewidth are commonly used to obtain fixed-parameter algorithms for NP-hard graph problems. For problems that are W[1]-hard parameterized by treewidth, a natural alternative would be to use a suitable analogue of ...
Cornelius Brand +4 more
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Journal of Algorithms, 1997
Summary: We consider a special variant of tree-decompositions, called domino tree-decompositions, and the related notion of domino treewidth. In a domino tree- decomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every \(k\), \(d\), there exists a constant \(c_{k,d}\) such that a graph with treewidth at ...
Hans L. Bodlaender, Joost Engelfriet
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Summary: We consider a special variant of tree-decompositions, called domino tree-decompositions, and the related notion of domino treewidth. In a domino tree- decomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every \(k\), \(d\), there exists a constant \(c_{k,d}\) such that a graph with treewidth at ...
Hans L. Bodlaender, Joost Engelfriet
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On Exact Algorithms for Treewidth
ACM Transactions on Algorithms, 2006We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential-time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time O
Bodlaender, Hans L. +4 more
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