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 -