{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article1651","name":"Power Assignment in Radio Networks with Two Power Levels","abstract":"We study the power assignment problem in radio networks, where each radio station can transmit in one of two possible power levels, corresponding to two ranges - short and long. We show that this problem is NP-hard, and present an O(n^2)-time assignment algorithm, such that the number of transmitters that are assigned long range by the algorithm is at most (11\/6) times the number of transmitters that are assigned long range by an optimal algorithm. We also present an (9\/5)-approximation algorithm for this problem whose running time is considerably higher.\r\n\r\nNext, we formulate and study the Minimum-Area Spanning Tree (MAST)problem: Given a set P of n points in the plane, find a spanning tree of P of minimum \"area,\" where the area of a spanning tree T is the area of the union of the n-1 disks whose diameters are the edges in T. We prove that the Euclidean minimum spanning tree of P is a constant-factor approximation for MAST. We then apply this result to obtain constant-factor approximations for the Minimum-Area Range Assignment (MARA) problem, for the Minimum-Area Connected Disk Graph (MACDG) problem, and for the Minimum-Area Tour (MAT) problem. The first problem is a variant of the power assignment problem in radio networks, the second problem is a related natural problem, and the third problem is a variant of the traveling salesman problem.","keywords":["Radio networks","power assignment","approximation algorithms","minimum spanning tree","disk graph"],"author":[{"@type":"Person","name":"Carmi, Paz","givenName":"Paz","familyName":"Carmi"},{"@type":"Person","name":"Katz, Matthew","givenName":"Matthew","familyName":"Katz"}],"position":3,"pageStart":1,"pageEnd":18,"dateCreated":"2007-06-01","datePublished":"2007-06-01","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Carmi, Paz","givenName":"Paz","familyName":"Carmi"},{"@type":"Person","name":"Katz, Matthew","givenName":"Matthew","familyName":"Katz"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06481.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume633","volumeNumber":6481,"name":"Dagstuhl Seminar Proceedings, Volume 6481","dateCreated":"2007-06-01","datePublished":"2007-06-01","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article1651","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume633"}}}