ABSTRACT
Motivated by a question from [6], we investigate the number of queries required for testing that an input graph G is isomorphic to a graph H that is given in advance. Our main result is that the more "complex" H is, the more queries it takes to test an input graph G for the property of being isomorphic to H. This is provided in terms of an upper bound and a lower bound on the number of queries, giving a relation between this number and a natural measure of the complexity of H.
- N. Alon, E. Fischer, M. Krivelevich and M. Szegedy, Efficient testing of large graphs, Combinatorica 20 (2000), 451--476.Google ScholarCross Ref
- N. Alon and J. H. Spencer, The probabilistic method. Wiley-Interscience (John Wiley & Sons), New York, 1992 (1st edition) and 2000 (2nd edition).Google Scholar
- M. Blum, M. Luby and R. Rubinfeld, Self-testing/correcting with applications to numerical problems. Journal of Computer and System Sciences 47 (1993), 549--595 (a preliminary version appeared in Proc. 22nd STOC, 1990). Google ScholarDigital Library
- E. Fischer, Testing graphs for colorability properties, Proceedings of the 12th ACM-SIAM SODA (2001), 873--882. Google ScholarDigital Library
- E. Fischer, The art of uninformed decisions: A primer to property testing, The Bulletin of the European Association for Theoretical Computer Science 75 (2001), 97--126.Google Scholar
- E. Fischer, G. Kindler, D. Ron, S. Safra, and A. Samorodnitsky, Testing juntas, Journal of Computer and System Sciences (43rd FOCS special issue), in press (a preliminary version appeared in Proc. 43rd FOCS, 2002). Google ScholarDigital Library
- E. Fischer and I. Newman, Testing of matrix properties, Proceedings of the 33rd ACM STOC (2001), 286--295. Google ScholarDigital Library
- O. Goldreich, S. Goldwasser and D. Ron, Property testing and its connection to learning and approximation, Journal of the ACM 45 (1998), 653--750 (a preliminary version appeared in Proc. 37th FOCS, 1996). Google ScholarDigital Library
- O. Goldreich and L. Trevisan, Three theorems regarding testing graph properties, Random Structures and Algorithms 23 (2003), 23--57. Google ScholarDigital Library
- D. Ron, Property testing (a tutorial), In: Handbook of Randomized Computing (S. Rajasekaran, P. M. Pardalos, J. H. Reif and J. D. P. Rolim eds), Kluwer Press (2001).Google Scholar
- R. Rubinfeld and M. Sudan, Robust characterization of polynomials with applications to program testing, SIAM Journal of Computing 25 (1996), 252--271 (first appeared as a technical report, Cornell University, 1993). Google ScholarDigital Library
- E. Szemerédi, Regular partitions of graphs, In: Proc. Colloque Inter. CNRS No. 260 (J. C. Bermond, J. C. Fournier, M. Las Vergnas and D. Sotteau eds.), 1978, 399--401.Google Scholar
Index Terms
- The difficulty of testing for isomorphism against a graph that is given in advance
Recommendations
Testing Graph Isomorphism
Two graphs $G$ and $H$ on $n$ vertices are $\epsilon$-far from being isomorphic if at least $\epsilon\binom{n}{2}$ edges must be added or removed from $E(G)$ in order to make $G$ and $H$ isomorphic. In this paper we deal with the question of how many ...
The Difficulty of Testing for Isomorphism against a Graph That Is Given in Advance
Motivated by a question from [E. Fischer, G. Kindler, D. Ron, S. Safra, and A. Samorodnitsky, J. Comput. System Sci., 68 (2004), pp. 753--787], we investigate the number of queries required for testing that an input graph G is isomorphic to a fixed ...
Every monotone graph property is testable
STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computingA graph property is called monotone if it is closed under taking (not necessarily induced) subgraphs (or, equivalently, if it is closed under removal of edges and vertices). Many monotone graph properties are some of the most well-studied properties in ...
Comments