Heuristics for Cycle Packing of Adjacency Graphs for Genomes with Repeated Genes

The Adjacency Graph is a structure used to model genomes in several rearrangement distance problems. In particular, most studies use properties of a maximum cycle packing of this graph to develop bounds and algorithms for rearrangement distance problems, such as the reversal distance and the Double Cut and Join (DCJ) distance. When each genome has no repeated genes, there exists only one cycle packing for the graph. However, when each genome may have repeated genes, the problem of finding a maximum cycle packing for the adjacency graph (Adjacency Graph Packing) is NP-hard. In this work, we developed a greedy random heuristic and a genetic algorithm heuristic for the Adjacency Graph Packing problem for genomes with repeated genes. We present experimental results and compare these heuristics with the SOAR framework. Furthermore, we show how the solutions from our algorithms can improve the estimation for the reversal distance when compared to the SOAR framework. Lastly, we applied our genetic algorithm heuristic in real genomic data to validate its practical use.