Counting Shortest Two Disjoint Paths in Cubic Planar Graphs with an NC Algorithm

Andreas Björklund, Thore Husfeldt

Publikation: Konference artikel i Proceeding eller bog/rapport kapitelKonferencebidrag i proceedingsForskningpeer review


Given an undirected graph and two disjoint vertex pairs s1 , t1 and s2 , t2 , the Shortest two disjoint paths problem (S2DP) asks for the minimum total length of two vertex disjoint paths connecting s1 with t1, and s2 with t2, respectively.
We show that for cubic planar graphs there are NC algorithms, uniform circuits of polynomial size and polylogarithmic depth, that compute the S2DP and moreover also output the number of such minimum length path pairs.
Previously, to the best of our knowledge, no deterministic polynomial time algorithm was known for S2DP in cubic planar graphs with arbitrary placement of the terminals. In contrast, the randomized polynomial time algorithm by Björklund and Husfeldt, ICALP 2014, for general graphs is much slower, is serial in nature, and cannot count the solutions.
Our results are built on an approach by Hirai and Namba, Algorithmica 2017, for a general- isation of S2DP, and fast algorithms for counting perfect matchings in planar graphs.
Titel29th International Symposium on Algorithms and Computation (ISAAC 2018)
Antal sider13
ForlagSchloss Dagstuhl--Leibniz-Zentrum für Informatik
ISBN (Elektronisk)ISBN 978-3-95977-094-1
StatusUdgivet - 2018
NavnLeibniz International Proceedings in Informatics


Dyk ned i forskningsemnerne om 'Counting Shortest Two Disjoint Paths in Cubic Planar Graphs with an NC Algorithm'. Sammen danner de et unikt fingeraftryk.