Topic
Clique problem
About: Clique problem is a research topic. Over the lifetime, 1252 publications have been published within this topic receiving 31280 citations.
Papers published on a yearly basis
Papers
TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Abstract: The maximum clique problem is a classical problem in combinatorial optimization which finds important applications in different domains. In this paper we try to give a survey of results concerning algorithms, complexity, and applications of this problem, and also provide an updated bibliography. Of course, we build upon precursory works with similar goals [39, 232, 266].
1,175 citations
TL;DR: Clique width is bound in terms of its tree width on the one hand, and of the clique width of its edge complement on the other, to reduce the complexity measure of graphs associated with hierarchical decompositions.
832 citations
TL;DR: A branch-and-bound algorithm for the maximum clique problem--which is computationally equivalent to the maximum independent (stable) set problem--is presented with the vertex order taken from a coloring of the vertices and with a new pruning strategy.
720 citations
TL;DR: The maximal clique problem has been solved by means of molecular biology techniques and the algorithm is highly parallel and has satisfactory fidelity, representing further evidence for the ability of DNA computing to solve NP-complete search problems.
Abstract: The maximal clique problem has been solved by means of molecular biology techniques. A pool of DNA molecules corresponding to the total ensemble of six-vertex cliques was built, followed by a series of selection processes. The algorithm is highly parallel and has satisfactory fidelity. This work represents further evidence for the ability of DNA computing to solve NP-complete search problems.
654 citations
1 Jan 1993
TL;DR: In this paper, a unified and elementary introduction to the standard characterizations of chordal graphs and clique trees is presented, as well as a detailed proof of all the results.
Abstract: Clique trees and chordal graphs have carved out a niche for themselves in recent work on sparse matrix algorithms, due primarily to research questions associated with advanced computer architectures. This paper is a unified and elementary introduction to the standard characterizations of chordal graphs and clique trees. The pace is leisurely, as detailed proofs of all results are included. We also briefly discuss applications of chordal graphs and clique trees in sparse matrix computations.
592 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 6 |
| 2024 | 18 |
| 2023 | 23 |
| 2022 | 54 |
| 2021 | 38 |
| 2020 | 48 |