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2005
IEEE

A Characterization of the (natural) Graph Properties Testable with One-Sided Error

10 years 5 months ago
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
The problem of characterizing all the testable graph properties is considered by many to be the most important open problem in the area of property-testing. Our main result in this paper is a solution of an important special case of this general problem; Call a property tester oblivious if its decisions are independent of the size of the input graph. We show that a graph property P has an oblivious one-sided error tester, if and only if P is (almost) hereditary. We stress that any ”natural” property that can be tested (either with one-sided or with two-sided error) can be tested by an oblivious tester. In particular, all the testers studied thus far in the literature were oblivious. Our main result can thus be considered as a precise characterization of the ”natural” graph properties, which are testable with one-sided error. One of the main technical contributions of this paper is in showing that any hereditary graph property can be tested with one-sided error. This general re...
Noga Alon, Asaf Shapira
Added 24 Jun 2010
Updated 24 Jun 2010
Type Conference
Year 2005
Where FOCS
Authors Noga Alon, Asaf Shapira
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