SubexponentialTime Algorithms for Maximum Independent Set in PtFree and BroomFree Graphs
Bacsó, Gábor and Lokshtanov, D and Marx, Dániel and Pilipczuk, M and Tuza, Zsolt (2019) SubexponentialTime Algorithms for Maximum Independent Set in PtFree and BroomFree Graphs. ALGORITHMICA, 81 (2). pp. 421438. ISSN 01784617 10.1007/s0045301804795

Text
Bacso_421_3424408_ny.pdf Download (612kB)  Preview 
Abstract
In algorithmic graph theory, a classic open question is 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., in: Proceedings of the twentyfifth annual ACMSIAM symposium on discrete algorithms, SODA 2014, Portland, OR, USA, January 57, 2014, pp 570581, 2014), and an algorithm for t = 6 announced recently (Grzesik et al. in Polynomialtime algorithm for maximum weight independent set on P6free graphs. CoRR, arXiv:1707.05491, 2017). Here we study the existence of subexponentialtime algorithms for the problem: we show that for any t >= 1, there is an algorithm for Maximum Independent Set on Ptfree graphs whose running time is subexponential in the number of vertices. Even for the weighted version MWIS, the problem is solvable in 2(O(root tn log n)) time on Ptfree graphs. For approximation of MIS in broomfree graphs, a similar time bound is proved. 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 the number of edges):
Item Type:  Article 

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:  14 Oct 2019 09:08 
Last Modified:  17 Nov 2021 14:04 
URI:  https://eprints.sztaki.hu/id/eprint/9823 
Update Item 