Dual Power Assignment via Second Hamiltonian Cycle

TL;DR

This paper presents an improved approximation algorithm for the dual power assignment problem in wireless networks, leveraging properties of second Hamiltonian cycles to achieve better cost efficiency and approximation ratios.

Contribution

It introduces a novel approach using second Hamiltonian cycle properties to enhance approximation ratios for dual power assignment problems.

Findings

Improved approximation ratio from 1.617 to 1.571.

Algorithm achieves a 1.522-approximation for symmetric directed graphs.

Utilizes properties of second Hamiltonian cycles for optimization.

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 $\frac{\pi^2}{6}-\frac{1}{36}+\epsilon\thickapprox 1.617$ to $\frac{11}{7}\thickapprox 1.571$. Moreover, we show that the algorithm of Khuller et al. for the strongly connected spanning subgraph problem, which achieves an approximation ratio of $1.61$, is $1.522$-approximation algorithm for symmetric directed graphs. The innovation of this paper is in achieving these results via utilizing interesting properties for the existence of a second Hamiltonian cycle.