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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max k-cover is the problem of selecting k subsets from F such that their union has maximum cardi-nality. Both these problems are NP-hard. We prove that (1 ? o(1)) ln n is a threshold below which(More)
It is well known that two prover proof systems are a convenient tool for establishing hardness of approximation results. In this paper, we show that two prover proof systems are also convenient starting points for establishing easiness of approximation results. Our approach combines the Feige-Lovv asz (STOC92) semideenite programming relaxation of one-round(More)
We investigate relations between average case complexity and the complexity of approximation. Our preliminary findings indicate that this is a research direction that leads to interesting insights. Under the assumption that refuting 3SAT is hard on average on a natural distribution, we derive hardness of approximation results for min bisection, dense(More)
We develop the algorithmic theory of vertex separators, and its relation to the embeddings of certain metric spaces. Unlike in the edge case, we show that embeddings into L<inf>1</inf> (and even Euclidean embeddings) are insufficient, but that the additional structure provided by many embedding theorems does suffice for our purposes.We obtain an(More)
The contribution of this paper is two-fold. First, a connection is established between approximating the size of the largest clique in a graph and multi-prover interactive proofs. Second, an efficient multi-prover interactive proof for NP languages is constructed, where the verifier uses very few random bits and communication bits. Last, the connection(More)