shortest paths in the plane with polygonal obstacles

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1、ShortestPathsinthePlanewithPolygonalObstaclesJAMESA.STORERBrwuksUniLwslty,Htiltham,MassachusettsANDJOHNH.REIFDakeUnl[er,slty,Dnrham,NorthCarolinaAbstmctWepresentapracticalalgorithmforfindingmimmum-lengthpathsbetweenpointsintheEuclideanplanewith(notnecessarilyconvex)polygonalobstacles.Pr]ortothisw

2、ork,thebestknownalgorithmforfindingtheshortestpathbetweentwopointsintheplanerequiredfl(n~logjt)t]mcand0(n~)space,where;Zdenotesthenumberofobstacleedges.AssummgthatatriangulationoraVoronoiLl]agramfortheobstaclespaceisprowdedwiththeinput(ifisnot,eitheronecanbeprecomputcdinO(nlogn)time),wepresentan(

3、Xkn)t]mealgorithm,whereIidenotesthenumberof“Aands”(connectedcomponents)]ntheobstaclespace.Thealgorithmusesonly0(/Z)spaceand,gwcnasourcepoints,producesan0(n)SIZCdatastructuresuchthatthedl

4、dm0(1)hme.Thealgorithmcandsobcusedtocomputeshortestpathsforthemovementofadisk(sothatoptimalmovementforarbltra~objectscanbecomputedtotheaccuracyofenclosingthemwiththesmallestpossibled]sk).CatcgcmesandSubjectDescriptors:F.2.2[AnalysisofAlgorithmsandProblemComplexity]:NonnumcrudAlgorithmsandProblems

5、GeneralTerms:Algorithms,PerformanceAdditionalKeyWordsandPhrases:Euclldeimplane,mmimalmovementproblem,motionplanning,mover’sproblem.polygonalobstacles,robotics,shortestpath1.IntroductionTheclassicalrnoler’sproblcr~lis:Givenasourcepointandadestinationpoi?ltalongwithasetofpolyhedralobstaclesintwoort

6、hreedimensionalEuclideanThisptipcrwascompletedinApr]l19S5[RelfandStorer,1985]andwassubmittedtothisjournalmJune1985;atthattimeandduringtheprecedingyearwhentheresearchwasundertaken,J.StorerwaspdrtiallysupportedbyNSFgruntnumberDCR84-03244andJ.Rclfwaspart]allysupportedbytheOfficeofNtwalRestxirchgrant

7、numberNOOO-14-80-C-0647,whilevisitingtheLaboratoryforComputerScienceatMITAuthors’~ddrcsses,J.A,Storer,ComputerScienceDepartment,CentcxforComplexSystems,BrarrdclsUnivcrs]ty.Waltharn,MA02254.J.HReif,ComputerScienceDepart