A polynomial time parallel algorithm for graph isomorphism using a quasipolynomial number of processors
Abstract
The Graph Isomorphism (GI) problem is a theoretically interesting problem because it has not been proven to be in P nor to be NPcomplete. Babai made a breakthrough in 2015 when announcing a quasipolynomial time algorithm for GI problem. Babai's work gives the most theoretically efficient algorithm for GI, as well as a strong evidence favoring the idea that class GI $\ne$ NP and thus P $\ne$ NP. Based on Babai's algorithm, we prove that GI can further be solved by a parallel algorithm that runs in polynomial time using a quasipolynomial number of processors. We achieve that result by identifying the bottlenecks in Babai's algorithms and parallelizing them. In particular, we prove that color refinement can be computed in parallel logarithmic time using a polynomial number of processors, and the $k$dimensional WL refinement can be computed in parallel polynomial time using a quasipolynomial number of processors. Our work suggests that Graph Isomorphism and GIcomplete problems can be computed efficiently in a parallel computer, and provides insights on speeding up parallel GI programs in practice.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.04638
 Bibcode:
 2020arXiv200204638P
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Distributed;
 Parallel;
 and Cluster Computing
 EPrint:
 ICALP conference submission preprint