eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-08-18
36:1
36:22
10.4230/LIPIcs.MFCS.2021.36
article
Parallel Polynomial Permanent Mod Powers of 2 and Shortest Disjoint Cycles
Datta, Samir
1
Jaiswal, Kishlaya
1
Chennai Mathematical Institute, India
We present a parallel algorithm for permanent mod 2^k of a matrix of univariate integer polynomials. It places the problem in ⨁L ⊆ NC². This extends the techniques of Valiant [Leslie G. Valiant, 1979], Braverman, Kulkarni and Roy [Mark Braverman et al., 2009] and Björklund and Husfeldt [Andreas Björklund and Thore Husfeldt, 2019] and yields a (randomized) parallel algorithm for shortest two disjoint paths improving upon the recent (randomized) polynomial time algorithm [Andreas Björklund and Thore Husfeldt, 2019].
We also recognize the disjoint paths problem as a special case of finding disjoint cycles, and present (randomized) parallel algorithms for finding a shortest cycle and shortest two disjoint cycles passing through any given fixed number of vertices or edges.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol202-mfcs2021/LIPIcs.MFCS.2021.36/LIPIcs.MFCS.2021.36.pdf
permanent mod powers of 2
parallel computation
graphs
shortest disjoint paths
shortest disjoint cycles