منابع مشابه
Splitting an Expander Graph
Let G V E be an r regular expander graph Certain algorithms for nding edge disjoint paths require the edges of G to be partitioned into E E E Ek so that the graphs Gi V Ei are each expanders In this paper we give a non constructive proof of a very good split plus an algorithm which improves on that given in Broder Frieze and Upfal Existence and construction of edge disjoint paths on expander gr...
متن کاملSpectral Graph Theory Lecture 12 Expander Codes
Our construction of error-correcting codes will exploit bipartite expander graphs (as these give a much cleaner construction than the general case). Let’s begin by examining what a bipartite expander graph should look like. It’s vertex set will have two parts, U and V , each having n vertices. Every vertex will have degree d, and every edge will go from a vertex in U to a vertex in V . In the s...
متن کاملExpander graph arguments for message-passing algorithms
We show how expander based arguments may be used to prove that message passing algorithms can correct a linear number of erroneous messages. The implication of this result is that when the block length is sufficiently large, once a message passing algorithm has corrected a sufficiently large fraction of the errors, it will eventually correct all errors. This result is then combined with known r...
متن کاملQuantum expanders from any classical Cayley graph expander
We give a simple recipe for translating walks on Cayley graphs of a group G into a quantum operation on any irrep of G. Most properties of the classical walk carry over to the quantum operation: degree becomes the number of Kraus operators, the spectral gap becomes the gap of the quantum operation (viewed as a linear map on density matrices), and the quantum operation is efficient whenever the ...
متن کاملCollisions for the LPS Expander Graph Hash Function
We analyse the hash function family based on walks in LPS Ramanujan graphs recently introduced by Charles et al. We present an algorithm for finding collisions that runs in quasi-linear time in the length of the hashed value. A concrete instance of the hash function is considered, based on a 100-digit prime. A short collision is given, together with implementation details.
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ژورنال
عنوان ژورنال: Journal of Algorithms
سال: 1999
ISSN: 0196-6774
DOI: 10.1006/jagm.1999.1023