Hfree graphs, Independent Sets, and subexponentialtime algorithms
Bacsó, Gábor and Marx, Dániel and Tuza, Zsolt (2017) Hfree graphs, Independent Sets, and subexponentialtime algorithms. In: 11th International Symposium on Parameterized and Exact Computation, IPEC 2016. Leibniz International Proceedings in Informatics, LIPIcs (63). Schloss Dagstuhl LeibnizZentrum für Informatik, Dagstuhl, 3:13:12. ISBN 9783959770231 10.4230/LIPIcs.IPEC.2016.3

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Abstract
It is an old open question in algorithmic graph theory to determine the complexity of the Maximum Independent Set problem on Ptfree graphs, that is, on graphs not containing any induced path on t vertices. So far, polynomialtime algorithms are known only for t ≤ 5 [Lokshtanov et al., SODA 2014, pp. 570581, 2014]. Here we study the existence of subexponentialtime algorithms for the problem: by generalizing an earlier result of Randerath and Schiermeyer for t = 5 [Discrete Appl. Math., 158 (2010), pp. 10411044], we show that for any t ≥ 5, there is an algorithm for Maximum Independent Set on Ptfree graphs whose running time is subexponential in the number of vertices. Scattered Set is the generalization of Maximum Independent Set where the vertices of the solution are required to be at distance at least d from each other. We give a complete characterization of those graphs H for which dScattered Set on Hfree graphs can be solved in time subexponential in the size of the input (that is, in the number of vertices plus number of edges): If every component of H is a path, then dScattered Set on Hfree graphs with n vertices and m edges can be solved in time 2(n+m) 1O(1/V (H)), even if d is part of the input. Otherwise, assuming ETH, there is no 2o(n+m)time algorithm for dScattered Set for any fixed d ≥ 3 on Hfree graphs with nvertices and medges. © 2016 Gábor Bacsó, Dániel Marx, and Zsolt Tuza.
Item Type:  Book Section 

Uncontrolled Keywords:  Graph theory; Time algorithms; Subexponential time; Subexponential algorithms; Polynomialtime algorithms; Maximum independent sets; Set theory; Polynomial approximation; Parameter estimation; Parallel processing systems; Graphic methods; subexponential algorithms; Scattered set; Independent set; Hfree graphs 
Subjects:  Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány 
Divisions:  Informatics Laboratory 
SWORD Depositor:  MTMT Injector 
Depositing User:  MTMT Injector 
Date Deposited:  05 Jan 2018 08:06 
Last Modified:  21 Jul 2019 13:48 
URI:  http://eprints.sztaki.hu/id/eprint/9314 
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