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Related Experiment Videos

Replicator equations, maximal cliques, and graph isomorphism.

M Pelillo1

  • 1Dipartimento di Informatica, Università Ca Foscari di Venezia, 30172 Venezia Mestre, Italy.

Neural Computation
|December 1, 1999
PubMed
Summary
This summary is machine-generated.

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This study introduces a novel energy-minimization framework for graph isomorphism, utilizing a maximum clique formulation. Replicator equations offer competitive results for solving this complex combinatorial problem.

Area of Science:

  • Computational Mathematics
  • Theoretical Computer Science
  • Graph Theory

Background:

  • The graph isomorphism problem is a fundamental challenge in computer science.
  • The maximum clique problem is closely related to graph isomorphism.
  • Previous formulations often lack a direct correspondence between solutions.

Purpose of the Study:

  • To develop a new energy-minimization framework for graph isomorphism.
  • To leverage a maximum clique formulation for solving graph isomorphism.
  • To establish a clear one-to-one correspondence between problem solutions.

Main Methods:

  • Formulating the maximum clique problem as a standard quadratic program, based on the Motzkin-Straus theorem.
  • Employing replicator equations, a class of dynamical systems from theoretical biology, to solve the quadratic program.

Related Experiment Videos

  • Comparing the performance of replicator equations against mean-field annealing heuristics.

    • Main Results:

    • A novel energy-minimization framework for graph isomorphism is presented.
    • The quadratic programming formulation ensures a direct correspondence with the combinatorial problem.
    • Replicator equations yield experimental results competitive with advanced heuristics, despite limitations.

    Conclusions:

    • The proposed framework offers an effective approach to graph isomorphism.
    • Replicator equations provide a viable and competitive method for solving the associated quadratic program.
    • This work bridges graph theory, optimization, and theoretical biology.