Discrete Applied Mathematics· 2026Q2
Strength of the upper bounds for the Edge-Weighted Maximum Clique Problem
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- Q2SCImago
- 2026year
Short summary
The three main upper bounds for the Edge-Weighted Maximum Clique Problem (EWMCP) are shown to be unbounded, meaning they cannot provide a performance guarantee for finding the optimal clique value.
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Key points
- The three primary upper bounds for EWMCP do not offer a performance guarantee as their ratio to the optimal value can be unbounded.
- For any two upper bounds, specific instances exist where one is strictly tighter than the other.
- Theoretical findings are validated by computational experiments on DIMACS and random instance datasets.
AI-generated from the title and abstract; the full text is not read.
Abstract
We theoretically and computationally compare the strength of the three main upper bounds from the literature on the optimal value of the Edge-Weighted Maximum Clique Problem (EWMCP). We provide a set of instances for which the ratio between any of the three upper bounds and the optimal value of the EWMCP is unbounded, showing that none of them can give a performance guarantee. We further analyze the relative strength among the three upper bounds by determining, for every choice of a ratio between any two of them, the largest values it can attain and providing families of instances for which such values can be reached. Our results show that, for each pair of upper bounds, there exist appropriately chosen instances on which either bound is tighter than the other. Our theoretical analysis is complemented by extensive computational experiments on two benchmark datasets: the standard DIMACS instances and randomly generated instances, providing practical insights into the empirical strength of the upper bounds.
The authors' abstract, as published at the source. Discrete Applied Mathematics, 2026 · DOI ↗
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Field: Computational Theory and Mathematics
Computational Theory and MathematicsComputer Science