Planar Graph Isomorphism Is in Log-Space-Reference-Cited by-同舟云学术

Planar Graph Isomorphism Is in Log-Space

Published:2022-06-30 Issue:2 Volume:14 Page:1-33
ISSN:1942-3454
Container-title:ACM Transactions on Computation Theory
language:en
Short-container-title:ACM Trans. Comput. Theory

Author:

Datta Samir¹^ORCID,Limaye Nutan²^ORCID,Nimbhorkar Prajakta¹^ORCID,Thierauf Thomas³^ORCID,Wagner Fabian⁴^ORCID

Affiliation:

1. Chennai Mathematical Institute, India

2. IT University of Copenhagen, Denmark

3. Aalen University, Germany

4. Ulm University, Germany

Abstract

Graph Isomorphism is the prime example of a computational problem with a wide difference between the best-known lower and upper bounds on its complexity. The gap between the known upper and lower bounds continues to be very significant for many subclasses of graphs as well.We bridge the gap for a natural and important class of graphs, namely, planar graphs, by presenting a log-space upper bound that matches the known log-space hardness. In fact, we show a stronger result that planar graphcanonizationis in log-space.

Funder

DFG

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Theory and Mathematics,Theoretical Computer Science

Link

https://dl.acm.org/doi/pdf/10.1145/3543686

Reference51 articles.

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2. The complexity of planarity testing

3. V. Arvind, Bireswar Das, and Johannes Köbler. 2008. A logspace algorithm for partial 2-tree canonization. In Computer Science Symposium in Russia (CSR). Springer, 40–51.

4. V. Arvind and Nikhil Devanur. 2004. Symmetry breaking in trees and planar graphs by vertex coloring. In the Nordic Combinatorial Conference (NORCOM). Department of Mathematical Sciences.