Conceitos Básicos
New SAT encodings based on partial-ordering models outperform traditional ILP formulations for graph coloring problems.
Resumo
The content discusses new SAT encodings for the graph coloring problem, comparing them to traditional ILP models. It evaluates the effectiveness of these encodings on benchmark sets, highlighting the superiority of partial-ordering-based SAT models over ILP formulations.
Introduction
Graph coloring problem (GCP) and bandwidth coloring problem (BCP) defined.
Importance of optimal color assignment in various applications.
State-of-the-art Encodings
Assignment-based ILP model (ASS-I) and its constraints.
Partial-ordering based model (POP-I) with ordering colors relative to vertices.
Hybrid partial-ordering model (POPH-I) combining aspects of both models.
Experimental Evaluation for GCP
Comparison of new SAT encodings (POP-S, POPH-S) with traditional ILP formulations.
Performance analysis on benchmark sets, showcasing superior results of SAT encodings.
Experimental Results for BCP
Introduction to new SAT encodings (POP-S-B, POPH-S-B).
Comparison with ILP formulations and constraint programming methods.
Evaluation on bandwidth coloring instances, highlighting efficiency of SAT encodings.
Estatísticas
For the widely studied GCP, we experimentally compare our new SAT encoding to the state-of-the-art approaches on the DIMACS benchmark set. Our evaluation confirms that this SAT encoding is effective for sparse graphs and even outperforms the state-of-the-art on some DIMACS instances.
Our computational experiments for the bandwidth coloring problem confirm that the new SAT encodings clearly outperform not only the classical assignment-based formulations but also the published state-of-the-art approaches.
Citações
"Finding an optimal coloring is known to be NP-hard."
"Our contribution suggests new SAT encodings based on partial-ordering models."