## Abstract

A power assignment is an assignment of transmission power to each of the wireless nodes of a wireless network, so that the induced graph satisfies some desired properties. The cost of a power assignment is the sum of the assigned powers. In this paper, we consider the dual power assignment problem, in which each wireless node is assigned a high- or low-power level, so that the induced graph is strongly connected and the cost of the assignment is minimized. We improve the best known approximation ratio from [Formula presented]−[Formula presented]+ϵ≈1.617 to [Formula presented]≈1.571. Moreover, we show that the algorithm of Khuller et al. [11] for the strongly connected spanning subgraph problem, which achieves an approximation ratio of 1.617, is 1.522-approximation algorithm for symmetric directed graphs. The innovation of this paper is in achieving these results by using interesting conditions for the existence of a second Hamiltonian cycle.

Original language | English |
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Pages (from-to) | 41-53 |

Number of pages | 13 |

Journal | Journal of Computer and System Sciences |

Volume | 93 |

DOIs | |

State | Published - 1 May 2018 |

## Keywords

- Approximation algorithm
- Computational geometry
- Power assignment

## ASJC Scopus subject areas

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