#### Publication Date

11-2015

#### 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 2^{n} options, while in graph isomorphism, we need to look for one of n! options, and n! is much larger than 2^{n}. 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.

## Comments

Technical Report: UTEP-CS-15-81

Published in

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