TY - GEN
T1 - Algorithmic aspects of property testing in the dense graphs model
AU - Goldreich, Oded
AU - Ron, Dana
PY - 2009
Y1 - 2009
N2 - In this paper we consider two basic questions regarding the query complexity of testing graph properties in the adjacency matrix model. The first question refers to the relation between adaptive and non-adaptive testers, whereas the second question refers to testability within complexity that is inversely proportional to the proximity parameter, denoted ∈. The study of these questions reveals the importance of algorithmic design (also) in this model. The highlights of our study are: A gap between the complexity of adaptive and non-adaptive testers. Specifically, there exists a (natural) graph property that can be tested using Õ(∈-) adaptive queries, but cannot be tested using O(∈-3/2) non-adaptive queries. In contrast, there exist natural graph properties that can be tested using Õ(∈-1) non-adaptive queries, whereas Ω(∈ -∈1) queries are required even in the adaptive case. We mention that the properties used in the foregoing conflicting results have a similar flavor, although they are of course different.
AB - In this paper we consider two basic questions regarding the query complexity of testing graph properties in the adjacency matrix model. The first question refers to the relation between adaptive and non-adaptive testers, whereas the second question refers to testability within complexity that is inversely proportional to the proximity parameter, denoted ∈. The study of these questions reveals the importance of algorithmic design (also) in this model. The highlights of our study are: A gap between the complexity of adaptive and non-adaptive testers. Specifically, there exists a (natural) graph property that can be tested using Õ(∈-) adaptive queries, but cannot be tested using O(∈-3/2) non-adaptive queries. In contrast, there exist natural graph properties that can be tested using Õ(∈-1) non-adaptive queries, whereas Ω(∈ -∈1) queries are required even in the adaptive case. We mention that the properties used in the foregoing conflicting results have a similar flavor, although they are of course different.
UR - http://www.scopus.com/inward/record.url?scp=70449704981&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-03685-9_39
DO - 10.1007/978-3-642-03685-9_39
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AN - SCOPUS:70449704981
SN - 3642036848
SN - 9783642036842
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 520
EP - 533
BT - Approximation, Randomization, and Combinatorial Optimization
T2 - 12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009
Y2 - 21 August 2009 through 23 August 2009
ER -