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We study optimization versions of Graph Isomorphism. Given two graphs G1, G2, we are interested in finding a bijection π from V (G1) to V (G2) that maximizes the number of matches (edges mapped to edges or non-edges mapped to non-edges). We give an n O(log n) time approximation scheme that for any constant factor α < 1, computes an α-approximation. We prove… (More)

Let G = S be a solvable permutation group given as input by the generating set S. I.e. G is a solvable subgroup of the symmetric group S n. We give a deterministic polynomial-time algorithm that computes an expanding generating set of size O(n 2) for G. More precisely, given a λ < 1, we can compute a subset T ⊂ G of size O(n 2) 1 λ O(1) such that the… (More)

We initiate a thorough study of distributed property testing – producing algorithms for the approximation problems of property testing in the CONGEST model. In particular, for the so-called dense graph testing model we emulate sequential tests for nearly all graph properties having 1-sided tests, while in the general and sparse models we obtain faster tests… (More)

We show here that every non-adaptive property testing algorithm making a constant number of queries, over a fixed alphabet, can be converted to a sample-based (as per [Gol-dreich and Ron, 2015]) testing algorithm whose average number of queries is a fixed, smaller than 1, power of n. Since the query distribution of the sample-based algorithm is not… (More)

Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In the extended conditional sampling model, the algorithm is also allowed to obtain samples from the restriction of the… (More)

We study the complexity of isomorphism testing for boolean functions that are represented by decision trees or decision lists. Our results are the following: • Isomorphism testing of rank 1 decision trees is complete for logspace. • For any constant r ≥ 2, isomorphism testing for rank r decision trees is polynomial-time equivalent to Graph Isomorphism. As a… (More)

Let G = S be a solvable subgroup of the symmetric group Sn given as input by the generator set S. We give a deterministic polynomial-time algorithm that computes an expanding generator set of size O(n 2) for G. As a byproduct of our proof, we obtain a new explicit construction of ε-bias spaces of size O(n poly(log d))(1 ε) O(1) for the groups Z n d .

Let G = S be a solvable permutation group of the symmetric group S n given as input by the generating set S. We give a deterministic polynomial-time algorithm that computes an expanding generating set of size O(n 2) for G. More precisely, the algorithm computes a subset T ⊂ G of size O(n 2)(1/λ) O(1) such that the undirected Cayley graph Cay(G, T) is a… (More)

Given two n-variable Boolean functions f and g, we study the problem of computing an ε-approximate isomorphism between them. I.e. a permutation π of the n variables such that f (x1, x2,. .. , xn) and g(x π(1) , x π(2) ,. .. , x π(n)) differ on at most an ε fraction of all Boolean inputs {0, 1} n. We give a randomized 2 O(√ n log(n/ε) O(d)) time algorithm… (More)

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