Combinatorial Approximations for Cluster Deletion: Simpler, Faster, and Better
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910422813114368 |
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| author | Balmaseda, Vicente Xu, Ying Cao, Yixin Veldt, Nate |
| author_facet | Balmaseda, Vicente Xu, Ying Cao, Yixin Veldt, Nate |
| contents | Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a tighter analysis of two previous approximation algorithms, improving their approximation guarantees from 4 to 3. Moreover, we show that both algorithms can be derandomized in a surprisingly simple way, by greedily taking a vertex of maximum degree in an auxiliary graph and forming a cluster around it. One of these algorithms relies on solving a linear program. Our final contribution is to design a new and purely combinatorial approach for doing so that is far more scalable in theory and practice. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_16131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorial Approximations for Cluster Deletion: Simpler, Faster, and Better Balmaseda, Vicente Xu, Ying Cao, Yixin Veldt, Nate Data Structures and Algorithms Machine Learning Social and Information Networks Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a tighter analysis of two previous approximation algorithms, improving their approximation guarantees from 4 to 3. Moreover, we show that both algorithms can be derandomized in a surprisingly simple way, by greedily taking a vertex of maximum degree in an auxiliary graph and forming a cluster around it. One of these algorithms relies on solving a linear program. Our final contribution is to design a new and purely combinatorial approach for doing so that is far more scalable in theory and practice. |
| title | Combinatorial Approximations for Cluster Deletion: Simpler, Faster, and Better |
| topic | Data Structures and Algorithms Machine Learning Social and Information Networks |
| url | https://arxiv.org/abs/2404.16131 |