### Abstract

This paper is concerned with a restricted version of minimum cost delay-constrained multicast in a network where each link has a delay and a cost. Given a source vertex s and p destination vertices t_{1}, t _{2},.... t_{p} together with p corresponding nonnegative delay constraints d_{1}, d_{2},... ,d_{p}, many QoS multicast problems seek a minimum cost multicast tree in which the delay along the unique s-t_{i} path is no more than d, for 1 ≤ 1 ≤ p. This problem is NP-hard even when the topology of the multicast tree is fixed. In this paper we show that every multicast tree has an underlying Steiner topology and that every minimum cost delay-constrained multicast tree corresponds to a minimum cost delay-constrained realization of a corresponding Steiner topology. We present a fully polynomial time approximation scheme for computing a minimum cost delay-constrained multicast tree under a Steiner topology. We also present computational results of a preliminary implementation to illustrate the effectiveness of our algorithm and discuss its applications.

Original language | English (US) |
---|---|

Pages (from-to) | 53-72 |

Number of pages | 20 |

Journal | Algorithmica (New York) |

Volume | 41 |

Issue number | 1 |

DOIs | |

State | Published - Oct 2004 |

### Fingerprint

### Keywords

- Computer communications
- Fully polynomial time approximation scheme
- Minimum cost delay-constrained network under a steiner topology
- Quality of service

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Applied Mathematics
- Safety, Risk, Reliability and Quality

### Cite this

**A polynomial time approximation scheme for minimum cost delay-constrained multicast tree under a steiner topology.** / Xue, Guoliang; Xiao, Wei.

Research output: Contribution to journal › Article

*Algorithmica (New York)*, vol. 41, no. 1, pp. 53-72. https://doi.org/10.1007/s00453-004-1119-9

}

TY - JOUR

T1 - A polynomial time approximation scheme for minimum cost delay-constrained multicast tree under a steiner topology

AU - Xue, Guoliang

AU - Xiao, Wei

PY - 2004/10

Y1 - 2004/10

N2 - This paper is concerned with a restricted version of minimum cost delay-constrained multicast in a network where each link has a delay and a cost. Given a source vertex s and p destination vertices t1, t 2,.... tp together with p corresponding nonnegative delay constraints d1, d2,... ,dp, many QoS multicast problems seek a minimum cost multicast tree in which the delay along the unique s-ti path is no more than d, for 1 ≤ 1 ≤ p. This problem is NP-hard even when the topology of the multicast tree is fixed. In this paper we show that every multicast tree has an underlying Steiner topology and that every minimum cost delay-constrained multicast tree corresponds to a minimum cost delay-constrained realization of a corresponding Steiner topology. We present a fully polynomial time approximation scheme for computing a minimum cost delay-constrained multicast tree under a Steiner topology. We also present computational results of a preliminary implementation to illustrate the effectiveness of our algorithm and discuss its applications.

AB - This paper is concerned with a restricted version of minimum cost delay-constrained multicast in a network where each link has a delay and a cost. Given a source vertex s and p destination vertices t1, t 2,.... tp together with p corresponding nonnegative delay constraints d1, d2,... ,dp, many QoS multicast problems seek a minimum cost multicast tree in which the delay along the unique s-ti path is no more than d, for 1 ≤ 1 ≤ p. This problem is NP-hard even when the topology of the multicast tree is fixed. In this paper we show that every multicast tree has an underlying Steiner topology and that every minimum cost delay-constrained multicast tree corresponds to a minimum cost delay-constrained realization of a corresponding Steiner topology. We present a fully polynomial time approximation scheme for computing a minimum cost delay-constrained multicast tree under a Steiner topology. We also present computational results of a preliminary implementation to illustrate the effectiveness of our algorithm and discuss its applications.

KW - Computer communications

KW - Fully polynomial time approximation scheme

KW - Minimum cost delay-constrained network under a steiner topology

KW - Quality of service

UR - http://www.scopus.com/inward/record.url?scp=10844296639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10844296639&partnerID=8YFLogxK

U2 - 10.1007/s00453-004-1119-9

DO - 10.1007/s00453-004-1119-9

M3 - Article

AN - SCOPUS:10844296639

VL - 41

SP - 53

EP - 72

JO - Algorithmica (New York)

JF - Algorithmica (New York)

SN - 0178-4617

IS - 1

ER -