Explicit OR-dispersers with polylogarithmic degree
UNSPECIFIED (1998) Explicit OR-dispersers with polylogarithmic degree. In: 27th Annual ACM Symposium on Theory of Computing, LAS VEGAS, NEVADA, MAY 29-JUN 01, 1995. Published in: JOURNAL OF THE ACM, 45 (1). pp. 123-154.Full text not available from this repository.
An (N, M, T)-OR-disperser is a bipartite multigraph G = (V, W, E) with \V\ = N, and \W\ = M, having the following expansion property: any subset of V having at least T vertices has a neighbor set of size at least M/2. For any pair of constants xi, lambda, 1 greater than or equal to xi > lambda greater than or equal to 0, any sufficiently large N, and for any T greater than or equal to 2((log N)xi), M less than or equal to 2((log N))(lambda), we give an explicit elementary construction of an (N, M, T)-OR-disperser such that the out-degree of any vertex in V is at most polylogarithmic in N. Using this with known applications of OR-dispersers yields several results. First, our construction implies that the complexity class Strong-RP defined by Sipser, equals RP. Second, for any fixed eta > 0, we give the first polynomial-time simulation of RP algorithms using the output of any "eta-minimally random" source. For any integral R > 0, such a source accepts a single request for an R-bit string and generates the string according to a distribution that assigns probability at most 2(-R eta) to any string. It is minimally random in the sense that any weaker source is insufficient to do a black-box polynomial-time simulation of RP algorithms.
|Item Type:||Conference Item (UNSPECIFIED)|
|Subjects:||Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software|
|Journal or Publication Title:||JOURNAL OF THE ACM|
|Publisher:||ASSOC COMPUTING MACHINERY|
|Official Date:||January 1998|
|Number of Pages:||32|
|Page Range:||pp. 123-154|
|Title of Event:||27th Annual ACM Symposium on Theory of Computing|
|Location of Event:||LAS VEGAS, NEVADA|
|Date(s) of Event:||MAY 29-JUN 01, 1995|
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