A Simple 4-Approximation Algorithm for Maximum Agreement Forests on Multiple Unrooted Binary Trees
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929499227029504 |
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| author | Dempsey, Jordan van Iersel, Leo Jones, Mark Zeh, Norbert |
| author_facet | Dempsey, Jordan van Iersel, Leo Jones, Mark Zeh, Norbert |
| contents | We present a simple 4-approximation algorithm for computing a maximum agreement forest of multiple unrooted binary trees. This algorithm applies LP rounding to an extension of a recent ILP formulation of the maximum agreement forest problem on two trees by Van Wersch al. We achieve the same approximation ratio as the algorithm of Chen et al. but our algorithm is extremely simple. We also prove that no algorithm based on the ILP formulation by Van Wersch et al. can achieve an approximation ratio of $4 - \varepsilon$, for any $\varepsilon > 0$, even on two trees. To this end, we prove that the integrality gap of the ILP approaches 4 as the size of the two input trees grows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Simple 4-Approximation Algorithm for Maximum Agreement Forests on Multiple Unrooted Binary Trees Dempsey, Jordan van Iersel, Leo Jones, Mark Zeh, Norbert Data Structures and Algorithms We present a simple 4-approximation algorithm for computing a maximum agreement forest of multiple unrooted binary trees. This algorithm applies LP rounding to an extension of a recent ILP formulation of the maximum agreement forest problem on two trees by Van Wersch al. We achieve the same approximation ratio as the algorithm of Chen et al. but our algorithm is extremely simple. We also prove that no algorithm based on the ILP formulation by Van Wersch et al. can achieve an approximation ratio of $4 - \varepsilon$, for any $\varepsilon > 0$, even on two trees. To this end, we prove that the integrality gap of the ILP approaches 4 as the size of the two input trees grows. |
| title | A Simple 4-Approximation Algorithm for Maximum Agreement Forests on Multiple Unrooted Binary Trees |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2409.08440 |