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- W3108527933 abstract "We consider the problem of sampling connected induced subgraphs of a given input graph G. Our first result is that an efficient algorithm to approximately sample connected induced subgraphs of a given size (the size is specified in the input) does not exist unless RP = NP. We then focus on the problem of approximately sampling connected induced subgraphs with a bias, more precisely we consider a distribution where the probability of a connected subgraph induced by (Ssubseteq V(G)) is proportional to (lambda ^{|S|}). When the input graph G has maximum degree d we identify a threshold (lambda _d=frac{(d-1)^{(d-1)}}{d^d}). For (0< lambda < lambda _d) there exists a trivial efficient sampler for the problem, and for (lambda _d<lambda <1) an efficient approximate sampler does not exist unless RP = NP. Finally, we show local Markov chains are unlikely to be effective at approximately sampling connected subgraphs." @default.
- W3108527933 created "2020-12-07" @default.
- W3108527933 creator A5087208118 @default.
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- W3108527933 date "2020-01-01" @default.
- W3108527933 modified "2023-09-23" @default.
- W3108527933 title "The Hardness of Sampling Connected Subgraphs" @default.
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- W3108527933 doi "https://doi.org/10.1007/978-3-030-61792-9_37" @default.
- W3108527933 hasPublicationYear "2020" @default.
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