A randomized parallel 3D convex hull algorithm for coarse grained multicomputers

We present a randomized parallel algorithm for constructing the 3D convex hull on a generic p-processor coarse grained multicomputer with arbitrary interconnection network and n/p local memory per processor, where ~ z p’+’ (for some arbitrarily small c > O). For any given set of n points in 3-space, the algorithm computes the 3D convex hull, with high probability, in 0(w) local computation time and 0(1 ) communication phases with at most 0(~) data sent/received by each processor. That is, with high probability, the algorithm computes the 3D convex hull of an arbitrary point set in time 0(* + I’~,P), where I’~,P denotes the time complexity of one communication phase. In the terminology of the BSP model, our algorithm requires, with high probability, O(1) supersteps and a synchronization period @(%). In the LogP model, the execution time of our algorithm is asymptotically optimaJ for several archit ect ures. ● This work was partially supported by the Natural Sciences and Engineering Research Council of Canada and the ESPRIT Basic Research Actions Nr. 7141 (ALCOM II). tschool of Computer Science, Carleton Univer.9ity, Ottawa, Canada KIS 5B6. Email: dehne@scs. carlet on. ca ~J@t. of Computer Science, York University, NOrth York, Canada M3J 1P3. Email: {deng, dyrnond}@cs .yorku. ca 5 Dept. of Computer Science, Utrecht University, 3508 TB Utrecht, The Netherlands. Email: andreas@cs .ruu. nl II School Of EE and Dept. of Computer Sci., Purdue University, West Lafayette, IN 47907, USA. Email: ashf aq~cs .purdue. edu Permission to make. digitirl/llarci copies of :111or p:~rt of [his nl:llcri:ll wiLhout fee is granted provided lhat the ct]pics ;Ire II(J1 m:ldc {Jr dis~l-il,~itcd for profit or commercial advantage, the ACM copyrighl/sccvcr notice, the title of the publication and its date appear, and notice is given that copyright is by permission of the Association for Computin: Machinery, Inc. (ACM). To copy otherwise, to repuhlish,[o post on servers or LO redistribute to lists, requires specific permission and/cor ftx, SPAA’95 Santa Bmlxm CA USA(”) 1995 ACM O-89791 -717-0/9.5/07.S3.50

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