# Ant Colony Optimization Approaches for the Tree t-Spanner Problem

### Manisha Israni, Shyam Sundar

#### Abstract

A tree $t$-spanner of a given connected graph is a spanning tree $T$ in which the ratio of distance between every pair of vertices is at most $t$ times their distance in the graph, where $t$ is a parameter known as stretch factor of $T$. The tree $t$-spanner problem deals with finding a spanning tree in a connected graph whose stretch factor is minimum amongst all spanning trees of the graph. For unweighted graph, this problem is $\mathcal{NP}$-Hard for any fixed $t \geq 4$, whereas for weighted graph, this problem is $\mathcal{NP}$-Hard for any fixed ~ $t > 1$. This paper concerns this problem for connected, undirected, and weighted graph and proposes three variants of ant colony optimization (ACO) approach for this problem. ACO approach is a swarm intelligence technique inspired by the foraging behavior of real ants. All three variants of ACO approach have been tested on a set of randomly generated graph instances. Computational results show the effectiveness of all three variants of ACO approach.

Download#### Paper Citation

#### in Harvard Style

Israni M. and Sundar S. (2017). **Ant Colony Optimization Approaches for the Tree t-Spanner Problem**.In *Proceedings of the 9th International Joint Conference on Computational Intelligence - Volume 1: IJCCI,* ISBN 978-989-758-274-5, pages 200-206. DOI: 10.5220/0006490002000206

#### in Bibtex Style

@conference{ijcci17,

author={Manisha Israni and Shyam Sundar},

title={Ant Colony Optimization Approaches for the Tree t-Spanner Problem},

booktitle={Proceedings of the 9th International Joint Conference on Computational Intelligence - Volume 1: IJCCI,},

year={2017},

pages={200-206},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006490002000206},

isbn={978-989-758-274-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Joint Conference on Computational Intelligence - Volume 1: IJCCI,

TI - Ant Colony Optimization Approaches for the Tree t-Spanner Problem

SN - 978-989-758-274-5

AU - Israni M.

AU - Sundar S.

PY - 2017

SP - 200

EP - 206

DO - 10.5220/0006490002000206