Ajwani, DeepakDeepakAjwaniSitchinava, NodariNodariSitchinavaZeh, NorbertNorbertZeh2019-04-102019-04-102011 IEEE2011-09-089780769543857http://hdl.handle.net/10197/9898The 2011 IEEE International Parallel & Distributed Processing Symposium (IPDPS), Anchorage, Alaska, 16-20 May 2011The parallel external memory (PEM) model has been used as a basis for the design and analysis of a wide range of algorithms for private-cache multi-core architectures. As a tool for developing geometric algorithms in this model, a parallel version of the I/O-efficient distribution sweeping framework was introduced recently, and a number of algorithms for problems on axis-aligned objects were obtained using this framework. The obtained algorithms were efficient but not optimal. In this paper, we improve the framework to obtain algorithms with the optimal I/O complexity of O(sort P(N) + K/PB) for a number of problems on axis-aligned objects, P denotes the number of cores/processors, B denotes the number of elements that fit in a cache line, N and K denote the sizes of the input and output, respectively, and sort P(N) denotes the I/O complexity of sorting N items using P processors in the PEM model. To obtain the above improvement, we present a new one-dimensional batched range counting algorithm on a sorted list of ranges and points that achieves an I/O complexity of O((N + K)/PB), where K is the sum of the counts of all the ranges. The key to achieving efficient load balancing among the processors in this algorithm is a new method to count the output without enumerating it, which might be of independent interest.en© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Parallel external memoryPEMMulticore algorithmsComputational geometryParallel distribution sweepingComputational modelingConference Publication10.1109/IPDPS.2011.1062019-04-01https://creativecommons.org/licenses/by-nc-nd/3.0/ie/