Power assignment problems in wireless communication: Covering points by disks, reaching few receivers quickly, and energy-efficient travelling salesman tours

Stefan Funke, Sören Laue, Rouven Naujoks, Zvi Lotker

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    2 Scopus citations

    Abstract

    A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem. This paper considers several problems of that kind; the first problem was studied before in [1,6] and aims to select and assign powers to k out of a total of n wireless network stations such that all stations are within reach of at least one of the selected stations. We show that the problem can be (1∈+∈ε) approximated by only looking at a small subset of the input, which is of size , i.e. independent of n and polynomial in k and 1/ε. Here d denotes the dimension of the space where the wireless devices are distributed, so typically d∈∈3 and describes the relation between the Euclidean distance between two stations and the power consumption for establishing a wireless connection between them. Using this coreset we are able to improve considerably on the running time of for the algorithm by Bilo et al. at ESA'05 ([6]) actually obtaining a running time that is linear in n. Furthermore we sketch how outliers can be handled in our coreset construction. The second problem deals with the energy-efficient, bounded-hop multicast operation: Given a subset C out of a set of n stations and a designated source node s we want to assign powers to the stations such that every node in C is reached by a transmission from s within k hops. Again we show that a coreset of size independent of n and polynomial in k, |C|, 1/ε exists, and use this to provide an algorithm which runs in time linear in n. The last problem deals with a variant of non-metric TSP problem where the edge costs are the squared Euclidean distances; this problem is motivated by data aggregation schemes in wireless sensor networks. We show that a good TSP tour under Euclidean edge costs can be very bad in the squared distance measure and provide a simple constant approximation algorithm, partly improving upon previous results in [5], [4].

    Original languageEnglish
    Title of host publicationDistributed Computing in Sensor Systems - 4th IEEE International Conference, DCOSS 2008, Proceedings
    Pages282-295
    Number of pages14
    DOIs
    StatePublished - 1 Jul 2008
    Event4th IEEE International Conference on Distributed Computing in Sensor Systems, DCOSS 2008 - Santorini Island, Greece
    Duration: 11 Jun 200814 Jun 2008

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume5067 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    Conference4th IEEE International Conference on Distributed Computing in Sensor Systems, DCOSS 2008
    Country/TerritoryGreece
    CitySantorini Island
    Period11/06/0814/06/08

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • General Computer Science

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