eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-30
72:1
72:16
10.4230/LIPIcs.ISAAC.2021.72
article
A Faster Algorithm for Maximum Flow in Directed Planar Graphs with Vertex Capacities
Enoch, Julian
1
Fox, Kyle
1
Mesica, Dor
2
Mozes, Shay
2
https://orcid.org/0000-0001-9262-1821
Department of Computer Science, University of Texas at Dallas, TX, USA
Efi Arazi School of Computer Science, The Interdisciplinary Center Herzliya, Israel
We give an O(k³ Δ n log n min(k, log² n) log²(nC))-time algorithm for computing maximum integer flows in planar graphs with integer arc and vertex capacities bounded by C, and k sources and sinks. This improves by a factor of max(k²,k log² n) over the fastest algorithm previously known for this problem [Wang, SODA 2019].
The speedup is obtained by two independent ideas. First we replace an iterative procedure of Wang that uses O(k) invocations of an O(k³ n log³ n)-time algorithm for maximum flow algorithm in a planar graph with k apices [Borradaile et al., FOCS 2012, SICOMP 2017], by an alternative procedure that only makes one invocation of the algorithm of Borradaile et al. Second, we show two alternatives for computing flows in the k-apex graphs that arise in our modification of Wang’s procedure faster than the algorithm of Borradaile et al. In doing so, we introduce and analyze a sequential implementation of the parallel highest-distance push-relabel algorithm of Goldberg and Tarjan [JACM 1988].
https://drops.dagstuhl.de/storage/00lipics/lipics-vol212-isaac2021/LIPIcs.ISAAC.2021.72/LIPIcs.ISAAC.2021.72.pdf
flow
planar graphs
vertex capacities