A Tabu Search-Based Approach for Finding the Optimal l-Clique Metric Generator Set in Graphs

Articles in Press

Document Type : Original Article

Authors

1 Dept. of Mathematics, Faculty of Basic Sciences, Velayat University, Iranshahr, Iran

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran

Abstract

In this paper, a Tabu Search-based algorithm is proposed to find the l-clique metric generator set in connected graphs. The algorithm aims to minimize the size of a set of vertices that can uniquely identify the l-cliques in the graph. This problem, as a generalization of the classical metric dimension, is NP-hard and requires heuristic optimization methods due to its computational complexity. The proposed algorithm uses a tabu list and generates neighboring sets to search for an optimal solution, and through an evaluation function, it minimizes the number of vertices with identical metric codes. The results demonstrate that this approach is highly effective in identifying group structures in complex networks, with potential applications in network analysis and data mining.

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Soft Computing Journal

Articles in Press, Accepted Manuscript
Available Online from 27 October 2025

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History

  • Receive Date: 11 November 2024
  • Revise Date: 28 May 2025
  • Accept Date: 01 July 2025

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