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- W2149592811 abstract "In general, constructing a locally-optimal structure is a little harder than constructing an arbitrary structure, but significantly easier than constructing a globally-optimal structure. A similar situation arises in listing. In counting, most problems are #P-complete, but in approximate counting we observe an interesting reversal of the pattern. Assuming that #BIS is not equivalent to #SAT under AP-reductions, we show that counting maximal independent sets in bipartite graphs is harder than counting maximum independent sets. Motivated by this, we show that various counting problems involving minimal separators are #SAT-hard to approximate. These problems have applications for constructing triangulations and phylogenetic trees. • Approximately counting maximal independent sets in a bipartite graph is #SAT-hard. • Replacing “maximal” by “maximum” yields #MAX-BIS, which is conjectured to be easier. • Normally “maximum” problems are harder to solve than “maximal” problems, not easier. • Approximately counting minimal separators in a bipartite graph is also #SAT-hard. • How often is the usual pattern reversed in approximate counting?" @default.
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- W2149592811 date "2016-09-01" @default.
- W2149592811 modified "2023-10-17" @default.
- W2149592811 title "Approximately counting locally-optimal structures" @default.
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- W2149592811 doi "https://doi.org/10.1016/j.jcss.2016.04.001" @default.
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