### Abstract

In this paper, we will study a special Connected Dominating Set (CDS) problem - between any two nodes in a network, there exists at least one shortest path, all of whose intermediate nodes should be included in a special CDS, named Minimum rOuting Cost CDS (MOC-CDS). Therefore, routing by MOC-CDS can guarantee that each routing path between any pair of nodes is also the shortest path in the network. Thus, energy consumption and delivery delay can be reduced greatly. CDS has been studied extensively in Unit Disk Graph (UDG) or Disk Graph (DG). However, nodes in networks may have different transmission ranges and some communications may be obstructed by obstacles. Therefore, we model network as a bidirectional general graph in this paper. We prove that constructing a minimum MOC-CDS in general graph is NP-hard. We also prove that there does not exist a polynomial-time approximation algorithm for constructing a minimum MOC-CDS with performance ratio ρlnδ, where ρ is an arbitrary positive number (ρ < 1) and δ is the maximum node degree in network. We propose a distributed heuristic algorithm (called as FlagContest) for constructing MOC-CDS with performance ratio (1 - ln2) + 2lnδ. Through extensive simulations, we show that the results of FlagContest is within the upper bound proved in this paper. Simulations also demonstrate that the average length of routing paths through MOC-CDS reduces greatly compared to regular CDSs.

Original language | English |
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Title of host publication | Proceedings - International Conference on Distributed Computing Systems |

Pages | 448-457 |

Number of pages | 10 |

DOIs | |

Publication status | Published - 2010 Aug 27 |

Event | 30th IEEE International Conference on Distributed Computing Systems, ICDCS 2010 - Genova, Italy Duration: 2010 Jun 21 → 2010 Jun 25 |

### Other

Other | 30th IEEE International Conference on Distributed Computing Systems, ICDCS 2010 |
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Country | Italy |

City | Genova |

Period | 10/6/21 → 10/6/25 |

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### Keywords

- Connected dominating set
- General graph
- NP-hard
- Obstacle
- Shortest path
- Virtual backbones
- Wireless network

### ASJC Scopus subject areas

- Computer Networks and Communications
- Hardware and Architecture
- Software

### Cite this

*Proceedings - International Conference on Distributed Computing Systems*(pp. 448-457). [5541660] https://doi.org/10.1109/ICDCS.2010.17