Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Babai, L., Luks, E.M.: Canonical labeling of graphs. In: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, STOC 1983, pp. 171–183. ACM Press, New York (1983)
Balcázar, J.L., Lozano, A., Torán, J.: The Complexity of Algorithmic Problems on Succinct Instances. Computer Science, Research and Applications. Springer US (1992)
Eiter, T., Gottlob, G., Mannila, H.: Adding disjunction to datalog (extended abstract). In: Proceedings of the Thirteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, PODS 1994, pp. 267–278. ACM Press, New York (1994)
Feigenbaum, J., Kannan, S., Vardi, M.Y., Viswanathan, M.: Complexity of Problems on Graphs Represented as OBDDs. In: Meinel, C., Morvan, M. (eds.) STACS 1998. LNCS, vol. 1373, pp. 216–226. Springer, Heidelberg (1998)
Fleischner, H., Mujuni, E., Paulusma, D., Szeider, S.: Covering Graphs with Few Complete Bipartite Subgraphs. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 340–351. Springer, Heidelberg (2007)
Fortnow, L., Reingold, N.: PP Is Closed under Truth-Table Reductions. Information and Computation 124(1), 1–6 (1996)
Galota, M., Vollmer, H.: Functions computable in polynomial space. Information and Computation 198(1), 56–70 (2005)
Galperin, H., Wigderson, A.: Succinct representations of graphs. Information and Control 56(3), 183–198 (1983)
Jahanjou, H., Miles, E., Viola, E.: Local reductions (2013)
Köbler, J., Schöning, U., Torán, J.: The graph isomorphism problem: its structural complexity. Birkhauser (August 1994)
Papadimitriou, C.H., Yannakakis, M.: A note on succinct representations of graphs. Information and Control 71(3), 181–185 (1986)
Schöning, U., Torán, J.: The Satisfiability Problem: Algorithms and Analyses. Lehmanns Media (2013)
Toran, J.: On the hardness of graph isomorphism. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, pp. 180–186 (2000)
Torán, J.: Reductions to Graph Isomorphism. Theory of Computing Systems 47(1), 288–299 (2008)
Veith, H.: Languages represented by Boolean formulas. Information Processing Letters 63(5), 251–256 (1997)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Das, B., Scharpfenecker, P., Torán, J. (2014). Succinct Encodings of Graph Isomorphism. In: Dediu, AH., Martín-Vide, C., Sierra-Rodríguez, JL., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2014. Lecture Notes in Computer Science, vol 8370. Springer, Cham. https://doi.org/10.1007/978-3-319-04921-2_23
Download citation
DOI: https://doi.org/10.1007/978-3-319-04921-2_23
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04920-5
Online ISBN: 978-3-319-04921-2
eBook Packages: Computer ScienceComputer Science (R0)