TY - GEN
T1 - Sub-exponential time parameterized algorithms for graph layout problems on digraphs with bounded independence number
AU - Misra, Pranabendu
AU - Saurabh, Saket
AU - Sharma, Roohani
AU - Zehavi, Meirav
N1 - Publisher Copyright:
© Pranabendu Misra, Saket Saurabh, Roohani Sharma, and Meirav Zehavi.
PY - 2018/12/1
Y1 - 2018/12/1
N2 - 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.
AB - 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.
KW - Bounded independence number digraph
KW - Directed cutwidth
KW - Directed feedback arc set
KW - Optimal linear arrangement
KW - Sub-exponential fixed-parameter tractable algorithms
UR - https://www.scopus.com/pages/publications/85060888704
U2 - 10.4230/LIPIcs.FSTTCS.2018.35
DO - 10.4230/LIPIcs.FSTTCS.2018.35
M3 - Conference contribution
AN - SCOPUS:85060888704
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2018
A2 - Ganguly, Sumit
A2 - Pandya, Paritosh
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2018
Y2 - 11 December 2018 through 13 December 2018
ER -