The vertices of a geometric network are points on the plane, and its edges straight line segments joining them. A geometric network is called planar if it contains no two edges that intersect other than perhaps at a common endpoint. In the remainder of this paper we will assume that all our graphs, unless otherwise stated, are planar geometric networks. Our main goal here is that of studying routing algorithms that take advantage of the location of the nodes of geometric networks. | Handbook of Wireless Networks and Mobile Computing Edited by Ivan Stojmenovic Copyright 2002 John Wiley Sons Inc. ISBNs 0-471-41902-8 Paper 0-471-22456-1 Electronic CHAPTER 18 Routing with Guaranteed Delivery in Geometric and Wireless Networks JORGE URRUTIA Instituto de Matemáticas Universidad Nacional Autonoma de Mexico INTRODUCTION Theverticesof a geometric network are points on the plane and its edges straight line segmentsjoimngtheniiA gnomnSricneSworkts called planar if it contains no two edges that intersect other than perhaps at a common endpoint. In the remainder of this paper we will assume that all our graphs unless otherwise stated are planar geometric networks. Our main goal here is that of studying routing algorithms that take advantage of the location of the nodes of geometric networks. Early papers on routing ignored information regarding the physical location of the nodes of the networks. With the advent of new technologies such asglobal positioning systems GPS the user s location is becoming common information that can be retrieved from GPS and then used to develop better routing algorithms. brother applicaOions wecmouse thelocationof onodeas part ofitslabel. This canm turn tombe usedtooPtninoOftcoeoi cording wlrelessoellular nei voi1 wstoid .r . ntodethaveltxed arcdhCarcotnrnunlt atlonnetav bkaronsiniof obol nbonenuV-oeCwarV ond yrnnlectianaí mabiin a- coa titat move osbival friviyanPconnecttOrouvP d isp lri a o hi manvoC there t vnOdii tr t a global p sOn mnasyrtransyllt w avert Ot obtai o rlrpoyvical iocationoioeographical mformytianrygarpmvutetsaod s vitchesoOanetvv rk ityi. intormation regarding the position of the nodes of a network can and indeed has been used tooOOtm oewronting ncOeanblthai rvOo pVwrogenO thismfo normOot of papereyr e oftcnting ylgaritVmrolinggoographioaldaaahaabbeen wstoen 3 r r la is t5 .
