Why the Graph Isomorphism Problem Is Easier Than Propositional Satisfiability: A Possible Qualitative Explanation

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow

Publication Date

11-2015

Comments

Technical Report: UTEP-CS-15-81

Published in International Journal of Contemporary Mathematical Sciences, 2016, Vol. 11, No. 3, pp. 97-103.

Abstract

A recent result has shown that the graph isomorphism problem can be solved in quasi-polynomial time, while the general belief is that only exponential time algorithms are possible for propositional satisfiability. This is somewhat counter-intuitive, since for propositional satisfiability, we need to look for one of 2ⁿ options, while in graph isomorphism, we need to look for one of n! options, and n! is much larger than 2ⁿ. Our qualitative explanation for this counter-intuitive fact comes from the fact that, in general, a graph isomorphism problem has a unique solution -- in contrast to propositional satisfiability which, in general, has many solutions -- and it is known that problems with unique solutions are often easier to solve.