| Autor: |
Dell, Holger, Husfeldt, Thore, Marx, Dániel, Taslaman, Nina, Wáhlen, Martin |
| Rok vydání: |
2012 |
| Předmět: |
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| Zdroj: |
ACM Trans. Algorithms 10(4): 21:1-21:32 (2014) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1145/2635812 |
| Popis: |
We show conditional lower bounds for well-studied #P-hard problems: (a) The number of satisfying assignments of a 2-CNF formula with n variables cannot be counted in time exp(o(n)), and the same is true for computing the number of all independent sets in an n-vertex graph. (b) The permanent of an n x n matrix with entries 0 and 1 cannot be computed in time exp(o(n)). (c) The Tutte polynomial of an n-vertex multigraph cannot be computed in time exp(o(n)) at most evaluation points (x,y) in the case of multigraphs, and it cannot be computed in time exp(o(n/polylog n)) in the case of simple graphs. Our lower bounds are relative to (variants of) the Exponential Time Hypothesis (ETH), which says that the satisfiability of n-variable 3-CNF formulas cannot be decided in time exp(o(n)). We relax this hypothesis by introducing its counting version #ETH, namely that the satisfying assignments cannot be counted in time exp(o(n)). In order to use #ETH for our lower bounds, we transfer the sparsification lemma for d-CNF formulas to the counting setting. |
| Databáze: |
arXiv |
| Externí odkaz: |
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