Banded structure in binary matrices

Abstract

A 0--1 matrix has a banded structure if both rows and columns can be permuted so that the non-zero entries exhibit a staircase pattern of overlapping rows. The concept of banded matrices has its origins in numerical analysis, where entries can be viewed as descriptions between the problem variables; the bandedness corresponds to variables that are coupled over short distances. Banded data occurs also in other applications, for example in the physical mapping problem of the human genome, in paleontological data, in network data and in the discovery of overlapping communities without cycles.