Representative families
Hadas Shachnai,Meirav Zehavi +1 more
TLDR
This work shows that a powerful technique for computing representative families leads to a unified approach for substantially improving the running times of parameterized algorithms for some classic problems, including k-Partial Cover, k-Internal Out-Branching, and Long Directed Cycle.About:
This article is published in Journal of Computer and System Sciences.The article was published on 2016-05-01 and is currently open access. It has received 19 citations till now. The article focuses on the topics: Uniform matroid & Cover (topology).read more
Citations
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Journal Article
Parameterized complexity of finding subgraphs with hereditary properties
Subhash Khot,Venkatesh Raman +1 more
TL;DR: This paper considers the parameterized complexity of the following problem under the framework introduced by Downey and Fellows and shows that if Π includes all independent sets but not all cliques or vice versa, then the problem is hard for the parameterization class W[1] and is fixed parameter tractable otherwise.
Journal Article
New Limits to Classical and Quantum Instance Compression.
TL;DR: It is shown that strong AND- or OR-compression for SAT would imply non-uniform, statistical zero-knowledge proofs for SAT-an even stronger and more unlikely consequence than NP ⊆ coNP/poly.
Journal ArticleDOI
Long directed (s,t)-path: FPT algorithm
TL;DR: A simple algorithm is presented that solves Long Directed ( s, t ) -Path in time O ⋆ ( 4.884 k ) and results in an improvement upon the previous fastest algorithm for Long Directing Cycle.
Proceedings Article
Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses
Holger Dell,Dieter van Melkebeek +1 more
TL;DR: In this paper, it was shown that if satisfiability for vertex cover is not in NP/poly, then the polynomial-time hierarchy collapses to its third level, which implies that the hierarchy collapses.
Journal ArticleDOI
Faster deterministic parameterized algorithm for k-Path
TL;DR: A deterministic algorithm for k-Path with time complexity O^*(2.554^k) is given, which improves the previously best deterministic algorithms for this problem of Zehavi [ESA 2015] whose time complexity is 2.597^k.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Proceedings ArticleDOI
Some simplified NP-complete problems
TL;DR: This paper shows that a number of NP-complete problems remain NP- complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP-complete.
Book ChapterDOI
How to Find Long Paths Efficiently
TL;DR: In this paper, the complexity of finding a long path in directed or undirected graphs was studied and an algorithm for finding a longest path with complexity O(K! · |V| · |E|) was proposed.
Proceedings ArticleDOI
Efficient computation of representative sets with applications in parameterized and exact algorithms
TL;DR: The efficient construction of a q-representative family of size at most (p-qp) in time bounded by a polynomial in (p+qp), t, and the time required for field operations is demonstrated to demonstrate how the efficientConstruction of representative families can be a powerful tool for designing single-exponential parameterized and exact exponential time algorithms.