Minimizing Flow Time in the Wireless Gathering Problem

📝 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.

💡 Analysis

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.

📄 Content

arXiv:0802.2836v1 [cs.DS] 20 Feb 2008 Symposium on Theoretical Aspects of Computer Science 2008 (Bordeaux), pp. 109-120 www.stacs-conf.org MINIMIZING FLOW TIME IN THE WIRELESS GATHERING PROBLEM VINCENZO BONIFACI 1,3, PETER KORTEWEG 2, ALBERTO MARCHETTI-SPACCAMELA 3, AND LEEN STOUGIE 2,4 1 Technische Universit¨at Berlin, Institut f¨ur Mathematik, Berlin, Germany 2 Eindhoven University of Technology, Dept of Mathematics and Computer Science, Eindhoven, The Netherlands E-mail address: p.korteweg@tue.nl,l.stougie@tue.nl 3 University of Rome “La Sapienza”, Dept of Computer and Systems Science, Rome, Italy E-mail address: bonifaci@dis.uniroma1.it,alberto@dis.uniroma1.it 4 CWI, Amsterdam, The Netherlands E-mail address: stougie@cwi.nl 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 maxi- mum flow time of a data packet. We prove that no polynomial time algorithm for this problem can have approximation ratio less than Ω(m1/3) when m packets have to be transmitted, unless P = NP. We then use resource augmentation to assess the perfor- mance 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.

1. Introduction Wireless networks are used in many areas of practical interest, such as mobile phone communication, ad-hoc networks, and radio broadcasting. Moreover, recent advances in miniaturization of computing devices equipped with short range radios have given rise to strong interest in sensor networks for their relevance in many practical scenarios (environ- ment control, accident monitoring etc.) [1, 16]. In many applications of wireless networks data gathering is a critical operation for extracting useful information from the operating environment: information collected from multiple nodes in the network should be transmitted to a sink that may process the data, or act as a gateway to other networks. We remark that in the case of wireless sensor networks 1998 ACM Subject Classification: C.2.2: Computer-Communication Networks – Network Protocols; F.2.2: Analysis of Algorithms and Problem Complexity – Nonnumerical Algorithms and Problems. General terms: Algorithms, Design, Theory. Key words and phrases: wireless networks, data gathering, approximation algorithms, distributed algorithms. c ⃝ V. Bonifaci, P. Korteweg, A. Marchetti-Spaccamela, and L. Stougie CC ⃝ Creative Commons Attribution-NoDerivs License 110 V. BONIFACI, P. KORTEWEG, A. MARCHETTI-SPACCAMELA, AND L. STOUGIE sensor nodes have limited computation capabilities, thus implying that data gathering is an even more crucial operation. For this reasons, data gathering in sensor networks has received significant attention in the last few years; we cite just a few contributions [1, 10]. The problem finds also applications in Wi-Fi networks when many users need to access a gateway using multi-hop wireless relay-routing [5]. In this paper we focus on the problem of designing and analysing simple distributed algorithms that have good approximation guarantees in realistic scenarios. Namely, we are interested in algorithms that are not only distributed but that are fast and can be implemented with limited overhead: sophisticated algorithms that require solving complex combinatorial optimization problems are impractical for implementations and have mainly theoretical interest. In order to formally assess the performance of the proposed algorithms we focus on the minimization of the maximum flow, i.e. minimizing the maximum time spent in the system by a packet. Almost all of the previous literature considered the objective of minimizing the completion time (see for example [3, 4, 5, 10, 11, 13, 17]). Flow minimization is a largely used criterion in scheduling theory that more suitably allows to assess the quality of service provided when multiple requests occur over time [7, 8, 12, 15]. The problem of modelling realistic scenarios of wireless sensor networks is complicated by the many parameters that define the communication among nodes and influence the performance of transmissions (see for example [1, 18]). In the sequel we assume that stations have a common clock, hence time can be divided into rounds. Each node is equipped with a half-duplex interface; as a result it cannot send and receive during the same round. Typically, not all nodes in the network can communicate with each other directly, hence packets have to be sent through several nodes before they can be gathered at the sink; this is called multi-hop routing. The key issue in our setting is interference. A radio signal has a transmission radius, the distance over which the signal is strong enough to send data, and an interference radius, the distance over which the radio signal is strong enough to interfere with other radio si

This content is AI-processed based on ArXiv data.