Approximately counting locally-optimal structures
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...
| Main Authors: | , , |
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| Format: | Journal article |
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Elsevier
2016
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| Summary: | 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. |
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