KD-Club: An Efficient Exact Algorithm with New Coloring-based Upper Bound for the Maximum k-Defective Clique Problem
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909067349327872 |
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| author | Jin, Mingming Zheng, Jiongzhi He, Kun |
| author_facet | Jin, Mingming Zheng, Jiongzhi He, Kun |
| contents | The Maximum k-Defective Clique Problem (MDCP) aims to find a maximum k-defective clique in a given graph, where a k-defective clique is a relaxation clique missing at most k edges. MDCP is NP-hard and finds many real-world applications in analyzing dense but not necessarily complete subgraphs. Exact algorithms for MDCP mainly follow the Branch-and-bound (BnB) framework, whose performance heavily depends on the quality of the upper bound on the cardinality of a maximum k-defective clique. The state-of-the-art BnB MDCP algorithms calculate the upper bound quickly but conservatively as they ignore many possible missing edges. In this paper, we propose a novel CoLoring-based Upper Bound (CLUB) that uses graph coloring techniques to detect independent sets so as to detect missing edges ignored by the previous methods. We then develop a new BnB algorithm for MDCP, called KD-Club, using CLUB in both the preprocessing stage for graph reduction and the BnB searching process for branch pruning. Extensive experiments show that KD-Club significantly outperforms state-of-the-art BnB MDCP algorithms on the number of solved instances within the cut-off time, having much smaller search tree and shorter solving time on various benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07235 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | KD-Club: An Efficient Exact Algorithm with New Coloring-based Upper Bound for the Maximum k-Defective Clique Problem Jin, Mingming Zheng, Jiongzhi He, Kun Data Structures and Algorithms The Maximum k-Defective Clique Problem (MDCP) aims to find a maximum k-defective clique in a given graph, where a k-defective clique is a relaxation clique missing at most k edges. MDCP is NP-hard and finds many real-world applications in analyzing dense but not necessarily complete subgraphs. Exact algorithms for MDCP mainly follow the Branch-and-bound (BnB) framework, whose performance heavily depends on the quality of the upper bound on the cardinality of a maximum k-defective clique. The state-of-the-art BnB MDCP algorithms calculate the upper bound quickly but conservatively as they ignore many possible missing edges. In this paper, we propose a novel CoLoring-based Upper Bound (CLUB) that uses graph coloring techniques to detect independent sets so as to detect missing edges ignored by the previous methods. We then develop a new BnB algorithm for MDCP, called KD-Club, using CLUB in both the preprocessing stage for graph reduction and the BnB searching process for branch pruning. Extensive experiments show that KD-Club significantly outperforms state-of-the-art BnB MDCP algorithms on the number of solved instances within the cut-off time, having much smaller search tree and shorter solving time on various benchmarks. |
| title | KD-Club: An Efficient Exact Algorithm with New Coloring-based Upper Bound for the Maximum k-Defective Clique Problem |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2308.07235 |