A heuristic algorithm solving the mutual-exclusivity-sorting problem

Motivation: Binary (or Boolean) matrices provide a common effective data representation adopted in several domains of computational biology, especially for investigating cancer and other human diseases. For instance, they are used to summarize genetic aberrations--copy number alterations or mutations--observed in cancer patientcohorts, effectively highlighting combinatorial relations among them. One of these is the tendency for two or more genes not to be co-mutated in the same sample or patient, i.e. a mutual-exclusivity trend. Exploiting this principle has allowed identifying new cancer driver protein-interaction networks and has been proposed to design effectivecombinatorial anti-cancer therapies rationally. Several tools exist to identify and statistically assess mutualexclusive cancer-driver genomic events. However, these tools need to be equipped with robust/efficient methods to sort rows and columns of a binary matrix to visually highlight possible mutual-exclusivity trends.Results: Here, we formalize the mutual-exclusivity-sorting problem and present MutExMatSorting: an R package implementing a computationally efficient algorithm able to sort rows and columns of a binary matrix to highlight mutual-exclusivity patterns. Particularly, our algorithm minimizes the extent of collective vertical overlap between consecutive non-zero entries across rows while maximizing the number of adjacent non-zero entries in the same row. Here, we demonstrate that existing tools for mutual-exclusivity analysis are suboptimal according to these criteria and are outperformed by MutExMatSorting.