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1、CompassRoutingonGeometricNetworksEvangelosKranakis,SchoolofComputerScience,CarletonUniversity,Ottawa,CanadaK1S5B6,HarvinderSingh,andJorgeUrrutia,SchoolofInformationTechnologyandEngineering,UniversityofOttawa,Ottawa,CanadaK1N6N51Introduction.incidentwiththevertexwearelocatedat.Startingats,
2、wewillinarecursivewaychooseandtraversetheSupposethatatravelerarrivestotheCityofToronto,edgeofourgeometricgraphincidenttoourcurrentandwantstowalktothefamousCN-Tower,oneofpositionandwiththeclosestslopetothatofthelinethetallestfree-standingstructuresintheworld.As-segmentconnectingthevertexwe
3、arestandingattosumenowthatourvisitor,lackingamapofToronto,t.Tiesarebrokenrandomly.isstandingatacrossingfromwhichhecanseetheCN-tower,andseveralstreetsS;:::;Sthathecan1mForthegraphshowninFigure2,compassroutingchoosetostarthiswalk.Anatural(andmostlikelywillproducethepaths,a,b,c,tfromstot.saf
4、eassumption),isthatourvisitormustchoosetowalk rstalongtheroadthatpointsclosestinthesdirectionoftheCN-tower,seeFigure1.Acloselookatmapsofnumerouscitiesaroundatheworld,showusthatthepreviouswaytoexploreanew,andunknowncitywillingeneralyieldwalksbthatwillbecloseenoughtotheoptimalonestotravelct
5、fromonelocationtoanother.Inmathematicalterms,wecanmodelthemapofmanycitiesbygeometricgraphsinwhichstreetinter-Figure2:Travelingfromstotusingcompassrouting.sectionsarerepresentedbytheverticesofourgraphs,andstreetsbystraightlinesegments.Compassrout-ingongeometricnetworks,initsmostelementalfo
6、rmInthispaperwestudylocalroutingalgorithmsonyieldsthefollowingalgorithm:geometricnetworks.Formallyspeaking,supposethatwewanttotravelfromavertexstoavertextofageometricnetwork.Aroutingalgorithmiscalledalocalroutingalgorithmifitsatis esthefollowingconditions:☞1.Ateachpointintime,weknowthecoo
7、rdinatesofourstartingposition,aswellasthoseofourdes-tination.Inaddition,wehaveatourdisposala niteamountofstoragewherewecankeepacon-Figure1:FindingourwaytotheCN-tower.stantnumberofidenti ersofverticesofournet-work.Noticethatthisimpliesthatatnopointintimedowehavefullk
