Partition of Eulerian graphs in circuits

Abstract

In this paper we will propose algorithms to solve the problem of partitioning the edge set of a graph into subsets, so that the subgraph induced by each subset of edges is a circuit, aiming to maximize the number of subsets of the partition. We will also design algorithms for a variation of this problem where the edges of the graph have colors (black or gray) and the subgraphs induced by the subsets of edges are alternating circuits, that is, consecutive edges in the circuit have different colors. We will investigate applications of these partitioning problems to the reverse ordering problem, which has great relevance in the area of computational biology in the study of evolutionary distance between species. We will develop models of integer linear programming to solve problems exactly and algorithms that use constructive heuristics and metaheuristics to obtain good solutions. Finally, we will conduct experiments to compare the performance of the algorithms we will present. (AU)