Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
نویسندگان
چکیده
منابع مشابه
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
We show that the size of the smallest depth-two N -superconcentrator is Θ(N log N/ log logN). Before this work, optimal bounds were known for all depths except two. For the upper bound, we build superconcentrators by putting together a small number of disperser graphs; these disperser graphs are obtained using a probabilistic argument. For obtaining lower bounds, we present two different method...
متن کاملTight Bounds for Depth-two Superconcentrators
We show that the minimum size of a depth-two N-superconcentrator is (N log 2 N= loglog N). Before this work, optimal bounds were known for all depths except two. For the upper bound, we build superconcentrators by putting together a small number of disperser graphs; these disperser graphs are obtained using a probabilistic argument. We present two diierent methods for showing lower bounds. Firs...
متن کاملTradeoffs in Depth-Two Superconcentrators
An N -superconcentrator is a directed graph with N input vertices and N output vertices and some intermediate vertices, such that for k = 1, 2, . . . , N , between any set of k input vertices and any set of k output vertices, there are k vertex disjoint paths. In a depth-two N -superconcentrator each edge either connects an input vertex to an intermediate vertex or an intermediate vertex to an ...
متن کاملOn Zarankiewicz Problem and Depth-Two Superconcentrators
We show tight necessary and sufficient conditions on the sizes of small bipartite graphs whose union is a larger bipartite graph that has no large bipartite independent set. Our main result is a common generalization of two classical results in graph theory: the theorem of Kővári, Sós and Turán on the minimum number of edges in a bipartite graph that has no large independent set, and the theore...
متن کاملSimulating Independence: New Constructions of Condensers, Ramsey Graphs, Dispersers, and Extractors Preliminary Full Version
A distribution X over binary strings of length n has min-entropy k if every string has probability at most 2−k in X. X is called a δ-source if its rate k/n is at least δ. We give the following new explicit constructions (namely, poly(n)-time computable functions) of deterministic extractors, dispersers and related objects. All work for any fixed rate δ > 0. No previous explicit construction was...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2000
ISSN: 0895-4801,1095-7146
DOI: 10.1137/s0895480197329508