Rejection sampling of bipartite graphs with given degree sequence

Acta Universitatis Sapientiae: Mathematica

Samee U.¹  Pirzada S.²  Khan Mohammad Ali³  Kayibi Koko K.⁴ 

[1] Department of Mathematics, Islamia College for Science and Commerce, Srinagar, India;Department of Mathematics, University of Kashmir, Srinagar, India;Department of Mathematics, University of Lethbridge, Canada;Department of Physics and Mathematics, University of Hull, UK;

关键词: degree sequence;    contraction of a degree sequence;    degree sequence bipartition;    contraction of a graph;    deletion of a graph;    ecological occurrence matrix;    05c07;    65c05;   

DOI  :  10.2478/ausm-2018-0020

来源: DOAJ

【 摘 要 】

Let A = (a1, a2, ..., an) be a degree sequence of a simple bipartite graph. We present an algorithm that takes A as input, and outputs a simple bipartite realization of A, without stalling. The running time of the algorithm is ⊝(n1n2), where ni is the number of vertices in the part i of the bipartite graph. Then we couple the generation algorithm with a rejection sampling scheme to generate a simple realization of A uniformly at random. The best algorithm we know is the implicit one due to Bayati, Kim and Saberi (2010) that has a running time of O(mamax), where m=12∑i=1nai$m = {1 \over 2}\sum\nolimits_{i = 1}^n {{a_i}} and amax is the maximum of the degrees, but does not sample uniformly. Similarly, the algorithm presented by Chen et al. (2005) does not sample uniformly, but nearly uniformly. The realization of A output by our algorithm may be a start point for the edge-swapping Markov Chains pioneered by Brualdi (1980) and Kannan et al.(1999).

【 授权许可】

Unknown