Minimizing Flow Time in the Wireless Gathering Problem

TL;DR

This paper investigates minimizing maximum flow time in wireless data gathering, proving computational hardness and analyzing a FIFO-like strategy's performance with resource augmentation.

Contribution

It establishes the hardness of approximating the problem and demonstrates that a FIFO-like strategy is 5-speed optimal under resource augmentation.

Findings

No polynomial algorithm can approximate within $ ilde{ ext{O}}(m^{1/3})$ unless P=NP.

A FIFO-like strategy is 5-speed optimal for minimizing flow time.

The analysis provides bounds on strategy performance with increased transmission speed.

Abstract

We address the problem of efficient data gathering in a wireless network through multi-hop communication. We focus on the objective of minimizing the maximum flow time of a data packet. We prove that no polynomial time algorithm for this problem can have approximation ratio less than $\Omega(m^{1/3)$ when $m$ packets have to be transmitted, unless $P = NP$. We then use resource augmentation to assess the performance of a FIFO-like strategy. We prove that this strategy is 5-speed optimal, i.e., its cost remains within the optimal cost if we allow the algorithm to transmit data at a speed 5 times higher than that of the optimal solution we compare to.