TY - GEN

T1 - Comparing the strength of query types in property testing

T2 - 19th Annual ACM-SIAM Symposium on Discrete Algorithms

AU - Ben-Eliezer, Ido

AU - Kaufman, Tali

AU - Krivelevich, Michael

AU - Ron, Dana

PY - 2008

Y1 - 2008

N2 - We study the power of four query models in the context of property testing in general graphs, where our main case study is the problem of testing k-colorability. Two query types, which have been studied extensively in the past, are pair queries and neighbor queries. The former corresponds to asking whether there is an edge between any particular pair of vertices, and the latter to asking for the i'th neighbor of a particular vertex. We show that while for pair queries, testing k-colorability requires a number of queries that is a monotone decreasing function in the average degree d, the query complexity in the case of neighbor queries remains roughly the same for every density and for large values of k. We also consider a combined model that allows both types of queries, and we propose a new, stronger, query model, which is related to the field of Group Testing. We give one-sided error upper and lower bounds for all the models, where the bounds are nearly tight for three of the models. In some of the cases our lower bounds extend to two-sided error algorithms. The problem of testing k-colorability was previously studied in the contexts of dense and sparse graphs, and in our proofs we unify approaches from those cases, and also provide some new tools and techniques which may be of independent interest.

AB - We study the power of four query models in the context of property testing in general graphs, where our main case study is the problem of testing k-colorability. Two query types, which have been studied extensively in the past, are pair queries and neighbor queries. The former corresponds to asking whether there is an edge between any particular pair of vertices, and the latter to asking for the i'th neighbor of a particular vertex. We show that while for pair queries, testing k-colorability requires a number of queries that is a monotone decreasing function in the average degree d, the query complexity in the case of neighbor queries remains roughly the same for every density and for large values of k. We also consider a combined model that allows both types of queries, and we propose a new, stronger, query model, which is related to the field of Group Testing. We give one-sided error upper and lower bounds for all the models, where the bounds are nearly tight for three of the models. In some of the cases our lower bounds extend to two-sided error algorithms. The problem of testing k-colorability was previously studied in the contexts of dense and sparse graphs, and in our proofs we unify approaches from those cases, and also provide some new tools and techniques which may be of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=58449104148&partnerID=8YFLogxK

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AN - SCOPUS:58449104148

SN - 9780898716474

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1213

EP - 1222

BT - Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 20 January 2008 through 22 January 2008

ER -