Abstract
We devise a framework for proving tight lower bounds under the counting exponential-time hypothesis #ETH introduced by Dell et al. (2014)
[18]. Our framework allows us to convert classical #P-hardness results for counting problems into tight lower bounds under #ETH, thus ruling out algorithms with running time 2o(n) graphs with n vertices and O(n) edges. As exemplary applications of this framework, we obtain tight lower bounds under #ETH for the evaluation of the zero-one permanent, the matching polynomial, and the Tutte polynomial on all non-easy points except for one line. This remaining line was settled very recently by Brand et al. (2016)
[18]. Our framework allows us to convert classical #P-hardness results for counting problems into tight lower bounds under #ETH, thus ruling out algorithms with running time 2o(n) graphs with n vertices and O(n) edges. As exemplary applications of this framework, we obtain tight lower bounds under #ETH for the evaluation of the zero-one permanent, the matching polynomial, and the Tutte polynomial on all non-easy points except for one line. This remaining line was settled very recently by Brand et al. (2016)
| Original language | English |
|---|---|
| Journal | Information and Computation |
| Volume | 261 |
| Pages (from-to) | 265-280 |
| Number of pages | 16 |
| ISSN | 0890-5401 |
| DOIs | |
| Publication status | Published - Aug 2018 |
| Externally published | Yes |
Keywords
- Tutte polynomial
- Independent set polynomial
- Matching polynomial
- Permanent
- Counting complexity
- Exponential-time hypothesis