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Given a collection<inline-equation><f> <sc>F</sc></f></inline-equation> of subsets of <?Pub Fmt italic>S<?Pub Fmt /italic> ={1,&#8230;,<?Pub Fmt italic>n<?Pub Fmt /italic>}, <?Pub Fmt italic>setcover<?Pub Fmt /italic> is the problem of selecting as few as possiblesubsets from <inline-equation> <f> <sc>F</sc></f></inline-equation> such that their union(More)
Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular functions is NP-hard.
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 Feage-Lovdsz (STOC92) semidefinite programming relaxation of one-round(More)
In this paper we extend the notion of zero knowledge proofs of membership (which reveal one bit of information) to zero knowledge proofs of knowledge (which reveal no information whatsoever). After formally defining this notion, we show its relevance to identification schemes, in which parties prove their identity by demonstrating their knowledge rather(More)
  • Uriel Feige
  • 2002
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)
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)
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)