Succinct Encodings of Graph Isomorphism
It is well known that problems encoded with circuits or formulas generally gain an exponential complexity blow-up compared to their original complexity.
We introduce a new way for encoding graph problems, based on CNF or DNF formulas. We show that contrary to the other existing succinct models, there are examples of problems whose complexity does not increase when encoded in the new form, or increases to an intermediate complexity class less powerful than the exponential blow up.
We also study the complexity of the succinct versions of the Graph Isomorphism problem. We show that all the versions are hard for PSPACE. Although the exact complexity of these problems is not known, we show that under most existing succinct models the different versions of the problem are equivalent. We also give an algorithm for the DNF encoded version of GI whose running time depends only on the size of the succinct representation.
KeywordsComplexity Succinct Graphisomorphism CNF DNF
Unable to display preview. Download preview PDF.
- 2.Balcázar, J.L., Lozano, A., Torán, J.: The Complexity of Algorithmic Problems on Succinct Instances. Computer Science, Research and Applications. Springer US (1992)Google Scholar
- 9.Jahanjou, H., Miles, E., Viola, E.: Local reductions (2013)Google Scholar
- 10.Köbler, J., Schöning, U., Torán, J.: The graph isomorphism problem: its structural complexity. Birkhauser (August 1994)Google Scholar
- 12.Schöning, U., Torán, J.: The Satisfiability Problem: Algorithms and Analyses. Lehmanns Media (2013)Google Scholar
- 13.Toran, J.: On the hardness of graph isomorphism. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, pp. 180–186 (2000)Google Scholar
- 16.Veith, H.: How to encode a logical structure by an OBDD. In: Proceedings of the 13th IEEE Conference on Computational Complexity, pp. 122–131. IEEE Comput. Soc. (1998)Google Scholar