Complexity and exact algorithms for vertex multicut in interval and bounded treewidth graphs

Guo, Jiong; Hüffner, Falk; Kenar, Erhan; Niedermeier, Rolf; Uhlmann, Johannes

doi:10.1016/j.ejor.2007.02.014

Cited by 34 publications

(24 citation statements)

References 23 publications

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“…The residual instance is defined by removing the layers congruent to i modulo p; each of its connected components is p-outerplanar, hence has bounded-treewidth. Guo et al [21,Corollary 1] show that vertex-weighted multiway cut (a generalization of our (edge-weighted) multiway cut since we can put weight ∞ on the original vertices and a vertex v e of weight w e on top of an original edge e of weight w e ) with a terminal set S on a graph G of treewidth p can be solved in O((|S| + 1) p+1 p 2 n) time by a standard dynamic program. Though this running time is sufficient for us to obtain a PTAS, it is not hard to see that the running time can be easily improved to p O(p) n 4 .…”

Section: A1 Reduction To Bounded-treewidth Graph After the Spanner Cmentioning

confidence: 99%

A Polynomial-time Approximation Scheme for Planar Multiway Cut

Bateni¹,

Hajiaghayi²,

Klein³

et al. 2012

Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms

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Given an undirected graph with edge lengths and a subset of nodes (called the terminals), a multiway cut (also called a multi-terminal cut) problem asks for a subset of edges with minimum total length and whose removal disconnects each terminal from the others. It generalizes the min st-cut problem but is NP-hard for planar graphs and APX-hard for general graphs. We give a polynomial-time approximation scheme for this problem on planar graphs. We prove the result by building a novel "spanner" for multiway cut on planar graphs which is of independent interest.

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Section: A1 Reduction To Bounded-treewidth Graph After the Spanner Cmentioning

confidence: 99%

A Polynomial-time Approximation Scheme for Planar Multiway Cut

Bateni¹,

Hajiaghayi²,

Klein³

et al. 2012

Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms

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“…The vertex multicut problem is NPcomplete for general directed graphs [15]. To solve it, we reduce it to the hitting set problem, which is also NP-complete, but for which good approximation algorithms are known [7].…”

Section: Definition 1 (Vertex Multicut)mentioning

confidence: 99%

“…To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. PLDI '12, June [11][12][13][14][15][16]2012, Beijing, China. Copyright c 2012 ACM 978-1-4503-1205-9/12/04.…”

Section: Introductionmentioning

confidence: 99%

Static analysis and compiler design for idempotent processing

2012

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Recovery functionality has many applications in computing systems, from speculation recovery in modern microprocessors to fault recovery in high-reliability systems. Modern systems commonly recover using checkpoints. However, checkpoints introduce overheads, add complexity, and often save more state than necessary.This paper develops a novel compiler technique to recover program state without the overheads of explicit checkpoints. The technique breaks programs into idempotent regions-regions that can be freely re-executed-which allows recovery without checkpointed state. Leveraging the property of idempotence, recovery can be obtained by simple re-execution. We develop static analysis techniques to construct these regions and demonstrate low overheads and large region sizes for an LLVM-based implementation. Across a set of diverse benchmark suites, we construct idempotent regions close in size to those that could be obtained with perfect runtime information. Although the resulting code runs more slowly, typical performance overheads are in the range of just 2-12%.The paradigm of executing entire programs as a series of idempotent regions we call idempotent processing, and it has many applications in computer systems. As a concrete example, we demonstrate it applied to the problem of compiler-automated hardware fault recovery. In comparison to two other state-of-the-art techniques, redundant execution and checkpoint-logging, our idempotent processing technique outperforms both by over 15%.

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“…Recently, the study of this type of problems from a parameterized complexity point of view has attracted a large amount of interest [5,7,13,[17][18][19][23][24][25][26][27]. Given a graph G and two vertices s and t of G, a subset of vertices S ⊆ V (G) \ {s, t} is an s-t separator if s and t appear in different connected components of the graph G − S. In separation problems, we are typically looking for small separators S. A natural extension of the problem is to demand G[S], i.e., the subgraph induced by S, to satisfy a certain property.…”

Section: Introductionmentioning

confidence: 99%

On the Parameterized Complexity of Finding Separators with Non-Hereditary Properties

et al. 2014

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Abstract. We study the problem of finding small s-t separators that induce graphs having certain properties. It is known that finding a minimum clique s-t separator is polynomial-time solvable (Tarjan 1985), while for example the problems of finding a minimum s-t separator that induces a connected graph or forms an independent set are fixed-parameter tractable when parameterized by the size of the separator (Marx, O'Sullivan and Razgon, ACM Trans. Algor., to appear). Motivated by these results, we study properties that generalize cliques, independent sets, and connected graphs, and determine the complexity of finding separators satisfying these properties. We investigate these problems also on bounded-degree graphs. Our results are as follows:(1) Finding a minimum c-connected s-t separator is FPT for c = 2 and W In order to prove (1), we show that the natural c-connected generalization of the wellknown Steiner Tree problem is FPT for c = 2 and W [1]-hard for any c ≥ 3.

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Complexity and exact algorithms for vertex multicut in interval and bounded treewidth graphs

Cited by 34 publications

References 23 publications

A Polynomial-time Approximation Scheme for Planar Multiway Cut

A Polynomial-time Approximation Scheme for Planar Multiway Cut

Static analysis and compiler design for idempotent processing

On the Parameterized Complexity of Finding Separators with Non-Hereditary Properties

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