Consecutive ones property testing: cut or swap

TL;DR

This paper introduces a simpler algorithm for testing the consecutive ones property in a family of subsets, utilizing a novel partitioning scheme to improve efficiency.

Contribution

A new, simpler algorithm for testing the consecutive ones property based on a novel partitioning scheme, reducing complexity compared to existing methods.

Findings

The algorithm effectively tests the consecutive ones property.

It simplifies the testing process with a new partitioning approach.

Potentially improves computational efficiency over previous algorithms.

Abstract

Let C be a finite set of $N elements and R = {R_1,R_2, ..,R_m} a family of M subsets of C. The family R verifies the consecutive ones property if there exists a permutation P of C such that each R_i in R is an interval of P. There already exist several algorithms to test this property in sum_{i=1}^m |R_i| time, all being involved. We present a simpler algorithm, based on a new partitioning scheme.