# On Maximum Weight Clique Algorithms, and How They Are Evaluated

@inproceedings{McCreesh2017OnMW, title={On Maximum Weight Clique Algorithms, and How They Are Evaluated}, author={Ciaran McCreesh and Patrick Prosser and Kyle Simpson and James Trimble}, booktitle={CP}, year={2017} }

Maximum weight clique and maximum weight independent set solvers are often benchmarked using maximum clique problem instances, with weights allocated to vertices by taking the vertex number mod 200 plus 1. For constraint programming approaches, this rule has clear implications, favouring weight-based rather than degree-based heuristics. We show that similar implications hold for dedicated algorithms, and that additionally, weight distributions affect whether certain inference rules are cost…

## 16 Citations

### Conflict Directed Clause Learning for Maximum Weighted Clique Problem

- Computer ScienceIJCAI
- 2018

This work proposes an efficient implementation of Babel's bound and pruning rule, as well as a novel dominance rule, based on SAT and on the "Conflict-Driven Clause Learning" (CDCL) algorithm.

### A new branch-and-bound algorithm for the Maximum Weighted Clique Problem

- MathematicsComput. Oper. Res.
- 2019

### Reduction and Local Search for Weighted Graph Coloring Problem

- Computer ScienceAAAI
- 2020

Techniques for solving WGCP are explored, including a lower bound and a reduction rule based on clique sampling, and a local search algorithm based on two selection rules and a new variant of configuration checking, resulting in the algorithm RedLS (Reduction plus Local Search).

### Improving Local Search for Minimum Weight Vertex Cover by Dynamic Strategies

- Computer ScienceIJCAI
- 2018

This work proposes two dynamic strategies that adjust the behavior of the algorithm during search, which are used to improve a state of the art local search for MWVC named FastWVC, resulting in two local search algorithms called DynW VC1 and DynWVC2.

### Improving the Performance of Stochastic Local Search for Maximum Vertex Weight Clique Problem Using Programming by Optimization

- Computer ScienceExpert Systems with Applications
- 2022

### A Semi-exact Algorithm for Quickly Computing A Maximum Weight Clique in Large Sparse Graphs

- Computer ScienceJ. Artif. Intell. Res.
- 2021

A new method for MWCP which interleaves clique finding with data reduction rules is proposed, and an algorithm called FastWClq is developed which finds better solutions than state-of-the-art algorithms while the running time of this algorithm is much shorter than the competitors for most instances.

### A Branch-and-Bound Based Exact Algorithm for the Maximum Edge-Weight Clique Problem

- Computer Science, MathematicsCSII
- 2018

An exact algorithm based on branch-and-bound for the maximum edge-weight clique problem, which is NP-hard, is proposed and confirmed to be faster than the methods based on mathematical programming.

### Certifying Solvers for Clique and Maximum Common (Connected) Subgraph Problems

- Computer ScienceCP
- 2020

This paper explains how state of the art maximum cliques, maximum weighted clique, maximal clique enumeration and maximum common (connected) induced subgraph algorithms can be turned into certifying solvers by using pseudo-Boolean models and cutting planes proofs.

### An Exact Algorithm for Minimum Weight Vertex Cover Problem in Large Graphs

- Computer ScienceArXiv
- 2019

Experiments on large graphs from real-world applications show that the reduction rules are effective and the resulting BMWVC algorithm outperforms relevant exact and heuristic MWVC algorithms.

### Advancing Tabu and Restart in Local Search for Maximum Weight Cliques

- Computer ScienceArXiv
- 2018

This paper improves the local search algorithms for solving the Maximum Weight Clique (MWC) problem by introducing new tabu and restart strategies, which outperforms several state-of-the-art solvers on the DIMACS, BHOSLIB, and two benchmarks from practical applications.

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