Superconcentrators of Depths 2 and 3; Odd Levels Help (Rarely)
نویسندگان
چکیده
It is shown that the minimum possible number of edges in an n-superconcentrator of depth 3 is Θ(n log log n), whereas the minimum possible number of edges in an n-superconcentrator of depth 2 is Ω(n(log n) 3/2) (and is O(n(log n) 2)).
منابع مشابه
Communication in Bounded Depth Circuits
We show that rigidity of matrices can be used to prove lower bounds on depth 2 circuits and communication graphs. We prove a general nonlinear lower bound on a certain type of circuits and thus, in particular, we determine the asymptotic size of depth d superconcentrators for all depths 4 (for even depths 4 it has been determined before).
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 کاملBounds 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 کاملSuperconcentrators
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comput. Syst. Sci.
دوره 48 شماره
صفحات -
تاریخ انتشار 1994