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- W2569149672 abstract "We present the fastest FPRAS for counting and randomly generating simple graphs with a given degree sequence in a certain range. For degree sequence $(d_i)_{i=1}^n$ with maximum degree $d_{max}=O(m^{1/4-tau})$, our algorithm generates almost uniform random graph with that degree sequence in time O(md max ) where is the number of edges in the graph and i¾?is any positive constant. The fastest known FPRAS for this problem [22] has running time of O(m3n2). Our method also gives an independent proof of McKay's estimate [33] for the number of such graphs.Our approach is based on sequential importance sampling(SIS) technique that has been recently successful for counting graphs [15,11,10]. Unfortunately validity of the SIS method is only known through simulations and our work together with [10] are the first results that analyze the performance of this method.Moreover, we show that for d= O(n1/2 i¾? i¾?), our algorithm can generate an asymptotically uniform d-regular graph. Our results are improving the previous bound of d= O(n1/3 i¾? i¾?) due to Kim and Vu [30] for regular graphs." @default.
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- W2569149672 date "2007-01-01" @default.
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- W2569149672 title "A Sequential Algorithm for Generating Random Graphs" @default.
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- W2569149672 doi "https://doi.org/10.1007/978-3-540-74208-1_24" @default.
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