Readability of digraphs and bipartite graphs

TL;DR

This paper explores the graph parameter called readability, focusing on digraphs and bipartite graphs, presenting algorithms for exact computation, bounds, and applications to specific graph classes like grids.

Contribution

It introduces algorithms for computing and bounding readability, including exact methods for grid graphs, and discusses the complexity and applications in bioinformatics.

Findings

Readability is small for graphs from genome sequencing.

An ILP-based method for exact readability computation.

Polynomial-time algorithm for grid graph overlap labeling.

Abstract

In the final project paper we consider a graph parameter called readability. Motivation for readability comes from bioinformatics applications. Graphs arising in problems related to genome sequencing are of small readability, which motivates the study of graphs of small readability. We present an algorithm due to Braga and Meidanis, which shows that every digraph is isomorphic to the overlap graph of some set of strings. An upper bound on readability is derived from the algorithm. The readability parameter can also be defined for bipartite graphs; in the final project paper special emphasis is given to the bipartite model. The complexity of computing the readability of a given digraph (or of a given bipartite graph) is unknown. A way for the exact computation of readability is presented using Integer Linear Programming. We also present two approaches for computing upper and lower bounds for readability due to Chikhi at al. Finally, the readability is computed exactly for toroidal and two-dimensional grid graphs and a polynomial time algorithm for constructing an optimal overlap labeling of a given two-dimensional or toroidal grid graph is presented.