Linear time algorithm for computing the rank of divisors on cactus graphs

TL;DR

This paper presents a linear time algorithm for computing the rank of divisors specifically on cactus graphs, addressing a problem known to be NP-hard in general.

Contribution

The paper introduces a novel linear time algorithm for calculating the rank of divisors on cactus graphs, a significant improvement over the NP-hard complexity in general graphs.

Findings

Linear time algorithm for cactus graphs

Efficient computation of divisor rank

Addresses NP-hardness in specific graph class

Abstract

Rank of divisor on graph was introduced in 2007 and it quickly attracts many attentions. Recently, in 2015 the problem for computing this quantity was proved to be NP-hard. In this paper, we describe a linear time algorithm for this problem limited on cactus graphs.