### Abstract

Connected dominating set (CDS) has played an important role in building virtual backbone, which is used on unicast, multicast, and fault-tolerant routing in wireless sensor networks. In order to reduce traffic congestion and communication delay, a routing-cost constrained minimum CDS (ROC–CDS) has been studied extensively in the literature. In this paper, we present a PTAS for αROC–CDS where α≥5, that is, there exists a polynomial-time (1+ε)-approximation for minimum CDS under constraint that for every pair of nodes u and v, m<inf>CDS</inf>(u,v)≤m(u,v) where m(u,v) denotes the number of intermediate nodes in the shortest path between u and v, and m<inf>CDS</inf>(u,v) denotes the number of intermediate nodes of the shortest path between u and v through CDS produced by the approximation algorithm.

Original language | English |
---|---|

Pages (from-to) | 18-26 |

Number of pages | 9 |

Journal | Journal of Combinatorial Optimization |

Volume | 30 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 Jul 28 |

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### Keywords

- Algorithm PTAS
- Growth bounded graphs
- Minimum connected dominating set
- Routing cost constraint

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Computational Theory and Mathematics
- Computer Science Applications
- Control and Optimization

### Cite this

*Journal of Combinatorial Optimization*,

*30*(1), 18-26. https://doi.org/10.1007/s10878-013-9626-8

**PTAS for routing-cost constrained minimum connected dominating set in growth bounded graphs.** / Wu, Lidong; Du, Hongwei; Wu, Weili; Zhu, Yuqing; Wang, Ailan; Lee, Wonjun.

Research output: Contribution to journal › Article

*Journal of Combinatorial Optimization*, vol. 30, no. 1, pp. 18-26. https://doi.org/10.1007/s10878-013-9626-8

}

TY - JOUR

T1 - PTAS for routing-cost constrained minimum connected dominating set in growth bounded graphs

AU - Wu, Lidong

AU - Du, Hongwei

AU - Wu, Weili

AU - Zhu, Yuqing

AU - Wang, Ailan

AU - Lee, Wonjun

PY - 2015/7/28

Y1 - 2015/7/28

N2 - Connected dominating set (CDS) has played an important role in building virtual backbone, which is used on unicast, multicast, and fault-tolerant routing in wireless sensor networks. In order to reduce traffic congestion and communication delay, a routing-cost constrained minimum CDS (ROC–CDS) has been studied extensively in the literature. In this paper, we present a PTAS for αROC–CDS where α≥5, that is, there exists a polynomial-time (1+ε)-approximation for minimum CDS under constraint that for every pair of nodes u and v, mCDS(u,v)≤m(u,v) where m(u,v) denotes the number of intermediate nodes in the shortest path between u and v, and mCDS(u,v) denotes the number of intermediate nodes of the shortest path between u and v through CDS produced by the approximation algorithm.

AB - Connected dominating set (CDS) has played an important role in building virtual backbone, which is used on unicast, multicast, and fault-tolerant routing in wireless sensor networks. In order to reduce traffic congestion and communication delay, a routing-cost constrained minimum CDS (ROC–CDS) has been studied extensively in the literature. In this paper, we present a PTAS for αROC–CDS where α≥5, that is, there exists a polynomial-time (1+ε)-approximation for minimum CDS under constraint that for every pair of nodes u and v, mCDS(u,v)≤m(u,v) where m(u,v) denotes the number of intermediate nodes in the shortest path between u and v, and mCDS(u,v) denotes the number of intermediate nodes of the shortest path between u and v through CDS produced by the approximation algorithm.

KW - Algorithm PTAS

KW - Growth bounded graphs

KW - Minimum connected dominating set

KW - Routing cost constraint

UR - http://www.scopus.com/inward/record.url?scp=84938213624&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938213624&partnerID=8YFLogxK

U2 - 10.1007/s10878-013-9626-8

DO - 10.1007/s10878-013-9626-8

M3 - Article

VL - 30

SP - 18

EP - 26

JO - Journal of Combinatorial Optimization

JF - Journal of Combinatorial Optimization

SN - 1382-6905

IS - 1

ER -