Generating Random Graphs Efficiently

We consider the algorithmic complexity of generating labeled (directed and undirected) graphs under various distributions. We describe three natural optimality criteria for graph generating algorithms, and show algorithms that are optimal for many distributions.

[1]  Bernard Chazelle,et al.  Optimal Solutions for a Class of Point Retrieval Problems , 1985, J. Symb. Comput..

[2]  Robert E. Tarjan,et al.  Efficiency of a Good But Not Linear Set Union Algorithm , 1972, JACM.

[3]  Frank Harary.  Chapter 1 – LABELED ENUMERATION , 1973 .

[4]  Voratas Kachitvichyanukul,et al.  Binomial random variate generation , 1988, CACM.

[5]  Alfred V. Aho,et al.  The design and analysis of algorithms , 1974 .

[6]  Nicholas C. Wormald,et al.  Generating Random Regular Graphs , 1984, J. Algorithms.

[7]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[8]  A. Nijenhuis.  Combinatorial algorithms , 1975 .

[9]  Frank Harary,et al.  Graphical enumeration , 1973 .

[10]  Mark Jerrum,et al.  Fast Uniform Generation of Regular Graphs , 1990, Theor. Comput. Sci..

[11]  Harold Neville Vazeille Temperley,et al.  Graph theory and applications , 1981 .

[12]  Robert E. Tarjan,et al.  A Linear-Time Algorithm for a Special Case of Disjoint Set Union , 1985, J. Comput. Syst. Sci..

[13]  Andrew Chi-Chih Yao,et al.  The complexity of nonuniform random number generation , 1976 .

[14]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[15]  Leslie G. Valiant,et al.  Random Generation of Combinatorial Structures from a Uniform Distribution , 1986, Theor. Comput. Sci..

[16]  Gottfried Tinhofer,et al.  Generating graphs uniformly at random , 1990 .

[17]  E. Palmer.  Graphical evolution: an introduction to the theory of random graphs , 1985 .

[18]  Paul F. Dietz,et al.  Two algorithms for maintaining order in a list , 1987, STOC.

[19]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[20]  Cecilia R. Aragon,et al.  Optimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning , 1989, Oper. Res..