Indexing moving points (extended abstract)

Abstract

WeproposethreeindexingschemesforstoringasetSofN pointsintheplane,eachmovingalongalineartrajectory,so thataqueryofthefollowingformcanbeansweredquickly: GivenarectangleRandarealvaluetq,reportallKpoints ofSthatlieinsideRattimetq.Werstpresentanindexing structurethat,foranygivenconstant">0,usesO(N=B) diskblocks,whereBistheblocksize,andanswersaqueryin O((N=B)1=2+"+K=B)I/Os.Itcanalsoreportallthepoints ofSthatlieinsideRduringagiventimeinterval.Apoint canbeinsertedordeleted,orthetrajectoryofapointcan bechanged,inO(log2BN)I/Os.Next,wepresentageneral approachthatimprovesthequerytimeifthequeriesarrive inchronologicalorder,byallowingtheindextoevolveover time.Weobtainatradeobetweenthequerytimeand thenumberoftimestheindexneedstobeupdatedasthe pointsmove.Wealsodescribeanindexingschemeinwhich thenumberofI/Osrequiredtoansweraquerydepends monotonicallyonthedierencebetweentqandthecurrent time.Finally,wedevelopanecientindexingschemeto answerapproximatenearest-neighborqueriesamongmoving points. CenterforGeometricComputing,DepartmentofComputer