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Candidate OneWay Functions Based on Expander Graphs
 IN ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY (ECCC
"... We suggest a candidate oneway function using combinatorial constructs such as expander graphs. These graphs are used to determine a sequence of small overlapping subsets of input bits, to which a hardwired random predicate is applied. Thus, the function is extremely easy to evaluate: All that is ..."
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Cited by 52 (1 self)
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We suggest a candidate oneway function using combinatorial constructs such as expander graphs. These graphs are used to determine a sequence of small overlapping subsets of input bits, to which a hardwired random predicate is applied. Thus, the function is extremely easy to evaluate: All
Iterative construction of cayley expander graphs
 THEORY OF COMPUTING
, 2005
"... We construct a sequence of groups Gn, and explicit sets of generators Yn ae Gn, such that all generating sets have bounded size, and the associated Cayley graphs are all expanders. The group G1 is the alternating group Ad, the set of even permutations on the elements {1, 2,..., d}. The group Gn ist ..."
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Cited by 6 (0 self)
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We construct a sequence of groups Gn, and explicit sets of generators Yn ae Gn, such that all generating sets have bounded size, and the associated Cayley graphs are all expanders. The group G1 is the alternating group Ad, the set of even permutations on the elements {1, 2,..., d}. The group Gn
EXPANDER GRAPHS FROM CURTISTITS GROUPS
"... Abstract. Using the construction of a nonorientable CurtisTits group of type Ãn, we obtain new explicit families of expander graphs of valency 5 for unitary groups over finite fields. ..."
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Abstract. Using the construction of a nonorientable CurtisTits group of type Ãn, we obtain new explicit families of expander graphs of valency 5 for unitary groups over finite fields.
Expander Graphs and Gaps between Primes
"... The explicit construction of infinite families of dregular graphs which are Ramanujan is known only in the case d−1 is a prime power. In this paper, we consider the case when d − 1 is not a prime power. The main result is that by perturbing known Ramanujan graphs and using results about gaps betwee ..."
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Cited by 2 (0 self)
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The explicit construction of infinite families of dregular graphs which are Ramanujan is known only in the case d−1 is a prime power. In this paper, we consider the case when d − 1 is not a prime power. The main result is that by perturbing known Ramanujan graphs and using results about gaps
ON COVERING EXPANDER GRAPHS BY HAMILTON CYCLES
, 2012
"... The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree ∆ satisfies some basic expansion properties and contain ..."
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Cited by 1 (0 self)
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The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree ∆ satisfies some basic expansion properties
Data stream algorithms via expander graphs
 In 19th International Symposium on Algorithms and Computation (ISAAC
, 2008
"... Abstract. We present a simple way of designing deterministic algorithms for problems in the data stream model via lossless expander graphs. We illustrate this by considering two problems, namely, ksparsity testing and estimating frequency of items. 1 ..."
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Cited by 4 (0 self)
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Abstract. We present a simple way of designing deterministic algorithms for problems in the data stream model via lossless expander graphs. We illustrate this by considering two problems, namely, ksparsity testing and estimating frequency of items. 1
Examples of Ramanujan and expander graphs for practical applications
, 2013
"... Expander graphs are highly connected sparse finite graphs. The property of being an expander seems significant in many of these mathematical, computational and physical contexts. Even more, expanders are surprizingly applicably applicable in other computational aspects: in the theory of error corec ..."
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Expander graphs are highly connected sparse finite graphs. The property of being an expander seems significant in many of these mathematical, computational and physical contexts. Even more, expanders are surprizingly applicably applicable in other computational aspects: in the theory of error
Codes and Iterative Decoding on Algebraic Expander Graphs
 INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY AND ITS APPLICATIONS HONOLULU, HAWAII, U.S.A., NOVEMBER 58, 2000
, 2000
"... The notion of graph expansion was introduced as a tool in coding theory by Sipset and Spielman, who used it to bound the minimum distance of a class of lowdensity codes, as well as the performance of various iterative decoding algorithms for these codes. In spite of its usefulness in establishing t ..."
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Cited by 15 (1 self)
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the use of explicit algebraic expander graphs and algebraic subcodes, and show that the resulting coding schemes achieve excellent performance, competitive with standard lowdensity paritycheck codes over a wide range of block lengths. Since the code constructions are based on graphs of groups
Expander graph arguments for message passing algorithms
 IEEE Trans. on Inform. Theory
, 2001
"... 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 fractio ..."
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Cited by 14 (3 self)
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algorithms, including Gallager’s hard decision and soft decision (with clipping) decoding algorithms. Our results assume low density parity check codes based on an irregular bipartite graph. Index Terms Low density parity check codes, expander graph, belief propagation, iterative decoding. I
Results 21  30
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1,337