Iterated Greedy Algorithms for the Hop-Constrained Steiner Tree Problem

TL;DR

This paper introduces three iterative greedy algorithms for the NP-hard Hop-Constrained Steiner Tree problem, including a novel Kruskal-based approach that significantly improves solution quality on benchmark instances.

Contribution

It presents a new Kruskal-inspired algorithm for HCST, the first application of such an approach under hop constraints, enhancing solution effectiveness.

Findings

Third algorithm reduces cost by 34.60% on dense graphs with hop 10.

Third algorithm reduces cost by 3.34% on sparse graphs with hop 3.

Proposed algorithms outperform Voss's method in effectiveness.

Abstract

The Hop-Constrained Steiner Tree problem (HCST) is challenging NP-hard problem arising in the design of centralized telecommunication networks where the reliability constraints matter. In this paper three iterative greedy algorithms are described to find efficient optimized solution to solve HCST on both sparse and dense graphs. In the third algorithm, we adopt the idea of Kruskal algorithm for the HCST problem to reach a better solution. This is the first time such algorithm is utilized in a problem with hop-constrained condition. Computational results on a number of problem instances are derived from well-known benchmark instances of Steiner problem in graphs. We compare three algorithms with a previously known method (Voss's algorithm) in term of effectiveness, and show that the cost of the third proposed method has been noticeably improved significantly, 34.60% in hop 10 on dense graphs and 3.34% in hop 3 on sparse graphs.