Recently, Razborov obtained superpolynomial lower bounds for monotone circuits that lect cliques in graphs. In particular, Razborov showed that detecting cliques of size s in a graph dh m vertices… (More)

Graph Bisection is the problem of partitioning the vertices of a graph into two equal-size pieces so as to minimize the number of edges between the two pieces. This paper presents an algorithm that… (More)

This paper surveys the recent results on the complexity of Boolean functions in terms of Boolean circuits, formulas, and branching programs. The primary aim is to give accessible proofs of the more… (More)

The amplification of probabilistic Boolean formulas refers to combining independent copies of such formulas to reduce the error probability. Les Valiant used the amplification method to produce… (More)

For a finite metric space V with a metric ρ, let V n be the metric space in which the distance between (a1, . . . , an) and (b1, . . . , bn) is the sum ∑n i=1 ρ(ai, bi). We obtain an asymptotic… (More)

The average sensitivity of a Boolean circuit is the expected number of input bits that, when flipped, change the output of the circuit, starting with a random input setting. We show that… (More)

We obtain tight bounds on the relative powers of the Priority and Common models of parallel random-access machines (PRAMs). Specifically we prove that:<list><item>The Element Distinctness function of… (More)

An approximation algorithm for the maximum independent set problem is given, improving the best performance guarantee known to O(n=(logn) 2 ). We also obtain the same performance guarantee for graph… (More)