منابع مشابه
Superconcentrators
An n-superconcentrator is an acyclic directed graph with n inputs and n outputs for which, for every -<_ n, every set of inputs, and every set of outputs, there exists an r-flow (a set of vertex-disjoint directed paths) from the given inputs to the given outputs. We show that there exist n-superconcentrators with 39n + O(log n) (in fact, at most 40n) edges, depth O(log n), and maximum degree (i...
متن کاملSuperconcentrators of Density 25.3
An N -superconcentrator is a directed, acyclic graph with N input nodes and N output nodes such that every subset of the inputs and every subset of the outputs of same cardinality can be connected by node-disjoint paths. It is known that linear-size and bounded-degree superconcentrators exist. We prove the existence of such superconcentrators with asymptotic density 25.3 (where the density is t...
متن کاملEigenvalues, Expanders and Superconcentrators
Explicit construction of families of linear expanders and superconcentrators is relevant to theoretical computer science in several ways. There is essentially only one known explicit construction. Here we show a correspondence between the eigenvalues of the adjacency matrix of a graph and its expansion properties, and combine it with results on Group Representations to obtain many new examples ...
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 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: Journal of Computer and System Sciences
سال: 1996
ISSN: 0022-0000
DOI: 10.1006/jcss.1996.0005