TY - GEN

T1 - An exponential time parameterized algorithm for planar disjoint paths

AU - Lokshtanov, Daniel

AU - Misra, Pranabendu

AU - Pilipczuk, Michal

AU - Saurabh, Saket

AU - Zehavi, Meirav

N1 - Funding Information:
∗This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant no. 819416, no. 715744 and no. 677651), United States–Israel Binational Science Foundation grant no. 2018302, Israel Science Foundation (ISF) individual research grant (grant no. 1176/18) and Swarnajayanti Fellowship grant DST/SJF/MSA-01/2017-18. †Additionally affiliated with University of Bergen, Norway and IRL 2000 ReLaX.
Publisher Copyright:
© 2020 ACM.

PY - 2020/6/8

Y1 - 2020/6/8

N2 - In the Disjoint Paths problem, the input is an undirected graph G on n vertices and a set of k vertex pairs, {si,ti}i=1k, and the task is to find k pairwise vertex-disjoint paths such that the i'th path connects si to ti. In this paper, we give a parameterized algorithm with running time 2O(k2)nO(1) for Planar Disjoint Paths, the variant of the problem where the input graph is required to be planar. Our algorithm is based on the unique linkage/treewidth reduction theorem for planar graphs by Adler et al. [JCTB 2017], the algebraic co-homology based technique developed by Schrijver [SICOMP 1994] for Disjoint Paths on directed planar graphs, and one of the key combinatorial insights developed by Cygan et al. [FOCS 2013] in their algorithm for Disjoint Paths on directed planar graphs. To the best of our knowledge our algorithm is the first parameterized algorithm to exploit that the treewidth of the input graph is small in a way completely different from the use of dynamic programming.

AB - In the Disjoint Paths problem, the input is an undirected graph G on n vertices and a set of k vertex pairs, {si,ti}i=1k, and the task is to find k pairwise vertex-disjoint paths such that the i'th path connects si to ti. In this paper, we give a parameterized algorithm with running time 2O(k2)nO(1) for Planar Disjoint Paths, the variant of the problem where the input graph is required to be planar. Our algorithm is based on the unique linkage/treewidth reduction theorem for planar graphs by Adler et al. [JCTB 2017], the algebraic co-homology based technique developed by Schrijver [SICOMP 1994] for Disjoint Paths on directed planar graphs, and one of the key combinatorial insights developed by Cygan et al. [FOCS 2013] in their algorithm for Disjoint Paths on directed planar graphs. To the best of our knowledge our algorithm is the first parameterized algorithm to exploit that the treewidth of the input graph is small in a way completely different from the use of dynamic programming.

KW - Disjoint paths

KW - Homology

KW - Network flow

KW - Parameterized complexity

KW - Planar graphs

UR - http://www.scopus.com/inward/record.url?scp=85086754930&partnerID=8YFLogxK

U2 - 10.1145/3357713.3384250

DO - 10.1145/3357713.3384250

M3 - Conference contribution

AN - SCOPUS:85086754930

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1307

EP - 1316

BT - STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing

A2 - Makarychev, Konstantin

A2 - Makarychev, Yury

A2 - Tulsiani, Madhur

A2 - Kamath, Gautam

A2 - Chuzhoy, Julia

PB - Association for Computing Machinery

T2 - 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020

Y2 - 22 June 2020 through 26 June 2020

ER -