An experimental evaluation of upper bounds of clique weights based on graph coloring | IEEE Conference Publication | IEEE Xplore

An experimental evaluation of upper bounds of clique weights based on graph coloring


Abstract:

The maximum weighted clique problem is the problem to find the clique whose sum of weights is maximum in vertex-weighted graphs. A branch and bound algorithm is often use...Show More

Abstract:

The maximum weighted clique problem is the problem to find the clique whose sum of weights is maximum in vertex-weighted graphs. A branch and bound algorithm is often used to solve this problem. A branch and bound algorithm solves the subproblems recursively to find the exact solution and can be faster by pruning subproblems which cannot improve the incumbent solution according to the upper bound. Greedy coloring is often used to find the upper bound of the maximum weighted clique problem. The coloring depends on vertex ordering and this affects the upper bound. In this paper, we propose an algorithm to obtain vertex ordering by using the smallest last ordering. We compared the proposed algorithm with a conventional method through some computational experiments using random graphs. Experimental results show that the proposed algorithm can get the exact solution faster than others for some sparse graphs.
Date of Conference: 14-16 December 2023
Date Added to IEEE Xplore: 19 March 2024
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Conference Location: Hochimin City, Vietnam

References

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