Journal of Combinatorial Theory Series A
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Practical loss-resilient codes
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the size of a random maximal graph
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Random Structures & Algorithms
On the origin of power laws in Internet topologies
ACM SIGCOMM Computer Communication Review
Network topology generators: degree-based vs. structural
Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications
Generating random regular graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Generating Random Regular Graphs Quickly
Combinatorics, Probability and Computing
On the Evolution of Triangle-Free Graphs
Combinatorics, Probability and Computing
Modern Coding Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs
IEEE Transactions on Information Theory
On the small cycle transversal of planar graphs
Theoretical Computer Science
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We present a simple and efficient algorithm for randomly generating simple graphs without small cycles. These graphs can be used to design high performance Low-Density Parity-Check (LDPC) codes. For any constant k, α ≤ 1/2k(k + 3) and m = O(n1+α), our algorithm generates an asymptotically uniform random graph with n vertices, m edges, and girth larger than k in polynomial time. To the best of our knowledge this is the first polynomial algorithm for the problem. Our algorithm generates a graph by sequentially adding m edges to an empty graph with n vertices. Recently, this type of sequential process has been very successful for efficiently counting and generating random graphs [35, 18, 11, 7, 5, 6].