Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-23T17:42:38.026Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-Deterministic Graph Property Testing

Published online by Cambridge University Press:  03 July 2013

LÁSZLÓ LOVÁSZ  and
KATALIN VESZTERGOMBI
LÁSZLÓ LOVÁSZ
Affiliation:
Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary (e-mail: lovasz@cs.elte.hu)
KATALIN VESZTERGOMBI
Affiliation:
Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary (e-mail: lovasz@cs.elte.hu)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A property of finite graphs is called non-deterministically testable if it has a ‘certificate’ such that once the certificate is specified, its correctness can be verified by random local testing. In this paper we study certificates that consist of one or more unary and/or binary relations on the nodes, in the case of dense graphs. Using the theory of graph limits, we prove that non-deterministically testable properties are also deterministically testable.

Keywords

Primary 05C85Secondary 68R1005C82
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 5 , September 2013 , pp. 749 - 762
Copyright
Copyright © Cambridge University Press 2013 

References

[1]Alon, N. and Shapira, A. (2008) A characterization of the (natural) graph properties testable with one-sided error. SIAM J. Comput. 37 1703–1727.CrossRefGoogle Scholar
[2]Alon, N., Fischer, E., Krivelevich, M. and Szegedy, M. (2000) Efficient testing of large graphs. Combinatorica 20 451–476.Google Scholar
[3]Alon, N., Fischer, E., Newman, I. and Shapira, A. (2006) A combinatorial characterization of the testable graph properties: It's all about regularity. In Proc. 38th ACM Symposium on the Theory of Computing: STOC, pp. 251–260.Google Scholar
[4]Arora, S., Karger, D. and Karpinski, M. (1995) Polynomial time approximation schemes for dense instances of NP-hard problems. In Proc. 27th ACM Symposium on the Theory of Computing, pp. 284–293.CrossRefGoogle Scholar
[5]Borgs, C., Chayes, J., Lovász, L., Sós, V. T. and Vesztergombi, K. (2006) Counting graph homomorphisms. In Topics in Discrete Mathematics (Klazar, M.et al., eds), Springer, pp. 315–371.Google Scholar
[6]Borgs, C., Chayes, J. T., Lovász, L., Sós, V. T. and Vesztergombi, K. (2008) Convergent graph sequences I: Subgraph frequencies, metric properties, and testing. Adv. Math. 219 1801–1851.Google Scholar
[7]Borgs, C., Chayes, J. T., Lovász, L., Sós, V. T. and Vesztergombi, K. (1912) Convergent graph sequences II: Multiway cuts and statistical physics. Ann. of Math. 176 151–219.CrossRefGoogle Scholar
[8]Elek, G. and Szegedy, B. Limits of hypergraphs, removal and regularity lemmas: A non-standard approach. arXiv:0705.2179Google Scholar
[9]Fischer, E. (2001) The art of uninformed decisions: A primer to property testing. The Computational Complexity Column of the Bulletin of the European Association for Theoretical Computer Science 75 97–126.Google Scholar
[10]Fischer, E. and Newman, I. (2005) Testing versus estimation of graph properties. In Proc. 37th ACM Symposium on the Theory of Computing, pp. 138–146.Google Scholar
[11]Frieze, A. and Kannan, R. (1999) Quick approximation to matrices and applications. Combinatorica 19 175–220.Google Scholar
[12]Goldreich, O., ed. (2010) Property Testing: Current Research and Surveys, Vol. 6390 of Lecture Notes in Computer Science, Springer.CrossRefGoogle Scholar
[13]Goldreich, O., Goldwasser, S. and Ron, D. (1998) Property testing and its connection to learning and approximation. J. Assoc. Comput. Mach. 45 653–750.Google Scholar
[14]Lovász, L. (2012) Large Networks and Graph Limits, AMS.Google Scholar
[15]Lovász, L. and Szegedy, B. (2006) Limits of dense graph sequences. J. Combin. Theory Ser. B 96 933–957.Google Scholar
[16]Lovász, L. and Szegedy, B. (2007) Szemerédi's Lemma for the analyst. Geom. Func. Anal. 17 252–270.Google Scholar
[17]Lovász, L. and Szegedy, B. (2010) Testing properties of graphs and functions. Israel J. Math. 178 113–156.Google Scholar
[18]Lovász, L. and Szegedy, B. Limits of compact decorated graphs. arXiv:1010.5155Google Scholar
[19]Rubinfeld, R. and Sudan, M. (1996) Robust characterization of polynomials with applications to program testing. SIAM J. Comput. 25 252–271.Google Scholar
[20]Saks, S. (1964) Theory of the Integral, Dover.Google Scholar