## Abstract

This work firstly studies the Steiner tree problem with bounded edge-length d in which d is the ratio of the maximum edge cost to the minimum edge cost. This work analyzes the algorithm of Byrka et al. [19] and shows that the approximation ratio of [Formula presented] for general graphs and approximation ratio of [Formula presented] for quasi-bipartite graphs. The algorithm implies approximation ratio of 1.162+ϵ for the problem on complete graphs with edge distances 1 and 2. This finding represents an improvement upon the previous best approximation ratio of 1.25. This work then presents a combinatorial two-phase heuristic for the general Steiner tree in greedy strategy that achieves an approximation ratio of 1.4295.

Original language | English |
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Pages (from-to) | 20-36 |

Number of pages | 17 |

Journal | Journal of Computer and System Sciences |

Volume | 123 |

DOIs | |

Publication status | Published - 2022 Feb |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics