FPT Algorithms for Connected Feedback Vertex Set

Misra, Neeldhara; Philip, Geevarghese; Raman, Venkatesh; Saurabh, Saket; Sikdar, Somnath

doi:10.1007/978-3-642-11440-3_25

Cited by 16 publications

(12 citation statements)

References 37 publications

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“…These include recent results by Kratsch and Wahlström [23], Cygan et al [10] and Misra et al [24] who used UNIQUE COVERAGE, STEINER TREE and CONNECTED VERTEX COVER and CONNECTED VERTEX COVER respectively as a starting point to obtain polynomial parameter transformations. In another development Dell and van Melkebeek [11] have obtained a strengthening of a result in [17] and using that they are able to show concrete lower bounds on problems that do admit polynomial kernels.…”

Section: Conclusion Discussion and Further Workmentioning

confidence: 99%

Incompressibility through Colors and IDs

Dom

Lokshtanov

Saurabh

2009

Automata, Languages and Programming

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144

141

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In parameterized complexity each problem instance comes with a parameter k, and a parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance to an instance with size polynomial in k. Many problems have been shown to admit polynomial kernels, but it is only recently that a framework for showing the non-existence of polynomial kernels for specific problems has been developed by Bodlaender et al. [6] and Fortnow and Santhanam [17]. With few exceptions, all known kernelization lower bounds result have been obtained by directly applying this framework. In this paper we show how to combine these results with combinatorial reductions which use colors and IDs in order to prove kernelization lower bounds for a variety of basic problems. Below we give a summary of our main results. All results are under the assumption that the polynomial hierarchy does not collapse to the third level.• We show that the STEINER TREE problem parameterized by the number of terminals and solution size k, and the CONNECTED VERTEX COVER and CAPACITATED VERTEX COVER problems do not admit a polynomial kernel. The two latter results are surprising because the closely related VERTEX COVER problem admits a kernel of with at most 2k vertices.• Alon and Gutner obtain a k poly(h) kernel for DOMINATING SET IN H -MINOR FREE GRAPHS parameterized by h = |H| and solution size k, and ask whether kernels of smaller size exist [3]. We partially resolve this question by showing that DOMINATING SET IN H -MINOR FREE GRAPHS does not admit a kernel with size polynomial in k + h.• Harnik and Naor obtain a "compression algorithm" for the SPARSE SUBSET SUM problem [21]. We show that their algorithm is essentially optimal by showing that the instances cannot be compressed further.• The HITTING SET and SET COVER problems are among the most studied problems in algorithmics. Both problems admit a kernel of size k O(d) when parameterized by solution size k and maximum set size d. We show that neither of them, along with the UNIQUE COVERAGE and BOUNDED RANK DISJOINT SETS problems, admits a polynomial kernel.The existence of polynomial kernels for several of the problems mentioned above were open problems explicitly stated in the literature [3,4,19,20,26]. Many of our results also rule out the existence of compression algorithms, a notion similar to kernelization defined by Harnik and Naor [21], for the problems in question.

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Section: Conclusion Discussion and Further Workmentioning

confidence: 99%

Incompressibility through Colors and IDs

Dom

Lokshtanov

Saurabh

2009

Automata, Languages and Programming

Self Cite

144

141

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“…-Algorithm Exact has the same O * running time as the best known parameterized algorithms for Subgraph Isomorphism, in which the subgraph is a tree [24], or has a bounded treewidth [16]. The same holds for group Steiner tree [26], and for Min Connected Components [29]. Indeed, all of these problems are special cases of PINQ I .…”

Section: Prior Work and Our Contributionmentioning

confidence: 94%

Improved Parameterized Algorithms for Network Query Problems

Pinter

Shachnai

Zehavi

2014

Parameterized and Exact Computation

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Abstract. Biological networks are often explored through extensive use of network queries. Partial Information Network Queries (PINQ) address the major challenge of analyzing such networks in the absence of certain topological data. In the PINQ problem, we are given a host graph H, modeling a network, and a pattern P, whose topology is only partially known. We seek a subgraph of H that resembles P. In this paper, we study a generalization of PINQ which allows near resemblance between H and P. We obtain an exact parameterized algorithm as well as an FPT-approximation scheme for a wide class of inputs, where the parameter is the number of nodes in P. Our algorithms substentially improve the best O * running times in solving PINQ, as well as the special cases of the Alignment Network Query problem and the Topology-Free Network Query problem.

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“…The problem is fixed-parameter tractable parameterized by the number of terminals (i.e., the size of S) [47]. Because any out-tree that contains all the vertices in S and also the vertex r must have at least |S| arcs, we obtain that |S| ≤ p. Consequently, the Directed Steiner Out-Tree problem is also fixed-parameter tractable parameterized by p instead of |S|.…”

Section: Directed Steiner Out-treementioning

confidence: 97%

A complete parameterized complexity analysis of bounded planning

Bäckström

Jönsson

Ordyniak

et al. 2015

Journal of Computer and System Sciences

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The propositional planning problem is a notoriously difficult computational problem, which remains hard even under strong syntactical and structural restrictions. Given its difficulty it becomes natural to study planning in the context of parameterized complexity. In this paper we continue the work initiated by Downey, Fellows and Stege on the parameterized complexity of planning with respect to the parameter "length of the solution plan." We provide a complete classification of the parameterized complexity of the planning problem under two of the most prominent syntactical restrictions, i.e., the so called PUBS restrictions introduced by Bäckström and Nebel and restrictions on the number of preconditions and effects as introduced by Bylander. We also determine which of the considered fixed-parameter tractable problems admit a polynomial kernel and which do not.

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FPT Algorithms for Connected Feedback Vertex Set

Cited by 16 publications

References 37 publications

Incompressibility through Colors and IDs

Incompressibility through Colors and IDs

Improved Parameterized Algorithms for Network Query Problems

A complete parameterized complexity analysis of bounded planning

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