eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-12-06
3:1
3:11
10.4230/LIPIcs.ISAAC.2018.3
article
Exploiting Sparsity for Bipartite Hamiltonicity
Björklund, Andreas
1
Department of Computer Science, Lund University, Sweden
We present a Monte Carlo algorithm that detects the presence of a Hamiltonian cycle in an n-vertex undirected bipartite graph of average degree delta >= 3 almost surely and with no false positives, in (2-2^{1-delta})^{n/2}poly(n) time using only polynomial space. With the exception of cubic graphs, this is faster than the best previously known algorithms. Our method is a combination of a variant of Björklund's 2^{n/2}poly(n) time Monte Carlo algorithm for Hamiltonicity detection in bipartite graphs, SICOMP 2014, and a simple fast solution listing algorithm for very sparse CNF-SAT formulas.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol123-isaac2018/LIPIcs.ISAAC.2018.3/LIPIcs.ISAAC.2018.3.pdf
Hamiltonian cycle
bipartite graph