eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-12-05
35:1
35:19
10.4230/LIPIcs.FSTTCS.2018.35
article
Sub-Exponential Time Parameterized Algorithms for Graph Layout Problems on Digraphs with Bounded Independence Number
Misra, Pranabendu
1
Saurabh, Saket
2
Sharma, Roohani
2
Zehavi, Meirav
3
University of Bergen, Norway
Institute of Mathematical Sciences, HBNI, India
Ben-Gurion University, Beersheba, Israel
Fradkin and Seymour [Journal of Combinatorial Graph Theory, Series B, 2015] defined the class of digraphs of bounded independence number as a generalization of the class of tournaments. They argued that the class of digraphs of bounded independence number is structured enough to be exploited algorithmically. In this paper, we further strengthen this belief by showing that several cut problems that admit sub-exponential time parameterized algorithms (a trait uncommon to parameterized algorithms) on tournaments, including Directed Feedback Arc Set, Directed Cutwidth and Optimal Linear Arrangement, also admit such algorithms on digraphs of bounded independence number. Towards this, we rely on the generic approach of Fomin and Pilipczuk [ESA, 2013], where to get the desired algorithms, it is enough to bound the number of k-cuts in digraphs of bounded independence number by a sub-exponential FPT function (Fomin and Pilipczuk bounded the number of k-cuts in transitive tournaments). Specifically, our main technical contribution is that the yes-instances of the problems above have a sub-exponential number of k-cuts. We prove this bound by using a combination of chromatic coding, an inductive argument and structural properties of the digraphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol122-fsttcs2018/LIPIcs.FSTTCS.2018.35/LIPIcs.FSTTCS.2018.35.pdf
sub-exponential fixed-parameter tractable algorithms
directed feedback arc set
directed cutwidth
optimal linear arrangement
bounded independence number digraph