Full text
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| Author(s): |
Breno Piva
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Computação |
| Defense date: | 2009-09-18 |
| Examining board members: |
Cid Carvalho de Souza;
Carlos Eduardo Ferreira;
Flávio Keidi Miyazawa
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| Advisor: | Cid Carvalho de Souza |
| Abstract | |
The Maximum Common Subgraph problem (MSIC) is in MV-hard and has applications in several fields. Despite its complexity, it is still important to know exact solutions for instances of this problem. The exact algorithms found in literature try to solve it through backtracking techniques or through its reduction to the Maximum Clique problem. In this work we try to give an exact solution to MSIC by addressing it directly, using Linear Integer Programming (PLI) and polyhedral combinatorics techniques. So, we performed a study of the MSIC polyhedron and we were able to find some strong valid inequalities, including some that were proven to define facets of that polyhedron. Additionally, we proved that an equivalence between the PLI model presented here for MSIC and a well known formulation for the Maximum Clique problem exists. Later, Branch-and-Bound (B&B) and Branch-and-Cut (B&C) algorithms were implemented using the inequalities found and some techniques to try to render the algorithms more efficient. Experiments were performed with the algorithms implemented in this work and, also, with an already existing algorithm to solve the Maximum Clique problem, called Cliquer. The results were compared and, among the PLI algorithms, we found that the most efficient was the one that used the formulation which we called Clique-IS, using B&B and more basic techniques than other algorithms. This algorithm was even more efficient than a PLI algorithm with a Clique-based model. This fact suggests that for a PLI approach it is worth to use a formulation based on the MSIC polyhedron instead of one based on its reduction to the Maximum Clique problem. The comparison of the best algorithm developed in this work with Cliquer, though, showed that the latest is more efficient. In order to some PLI-based algorithm (using a formulation with the same variables used by us) to have any chance of outperforming a combinatorial algorithm like Cliquer, it would be necessary to know more inequalities that are active in the problem's optimal solution (AU) | |