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- W2944770995 abstract "In a recent work (ECCC, TR18-171, 2018), we introduced models of testing graph properties in which, in addition to answers to the usual graph-queries, the tester obtains {em random vertices drawn according to an arbitrary distribution $D$}. Such a tester is required to distinguish between graphs that have the property and graphs that are far from having the property, {em where the distance between graphs is defined based on the unknown vertex distribution $D$}. These (vertex-distribution free (VDF)) models generalize the standard models in which $D$ is postulated to be uniform on the vertex-set, and they were studies both in the dense graph model and in the bounded-degree graph model. The focus of the aforementioned work was on testers, called {sf strong}, whose query complexity depends only on the proximity parameter $epsilon$. Unfortunately, in the standard bounded-degree graph model, some natural properties such as Bipartiteness do not have strong testers, and others (like cycle-freeness) do not have strong testers of one-sided error (whereas one-sided error was shown inherent to the VDF model). Hence, it was suggested to study general (i.e., non-strong) testers of sub-linear complexity. In this work, we pursue the foregoing suggestion, but do so in a model that augments the model presented in the aforementioned work. Specifically, we provide the tester with an evaluation oracle to the unknown distribution $D$, in addition to samples of $D$ and oracle access to the tested graph. Our main results are testers for Bipartitness and cycle-freeness, in this augmented model, having complexity that is almost-linear in the square root of the effective support size of $D$." @default.
- W2944770995 created "2019-05-16" @default.
- W2944770995 creator A5013698877 @default.
- W2944770995 date "2019-05-08" @default.
- W2944770995 modified "2023-09-27" @default.
- W2944770995 title "Testing Bipartitness in an Augmented VDF Bounded-Degree Graph Model" @default.
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