I/O-optimal Algorithms for Orthogonal Problems for Private-Cache Chip Multiprocessors

The parallel external memory (PEM) model has been used as a basis for the design and analysis of a wide range of algorithms for the private-cache multi-core architectures. Recently a parallel version of the distribution sweeping framework was introduced to efficiently solve a number of orthogonal geometric problems in the PEM model. In this paper we improve the framework to the optimal O(sortP (N)+K/PB) I/Os, where P is the number of cores/processors, B is the number of elements that fit into a cache-line, N and K are the sizes of the input and output, respectively, and sortP (N) denotes the I/O complexity of sorting N items on a P -processor PEM model. We achieve this with a new one-dimensional batched range counting algorithm on a sorted list of ranges and points that achieves O((N + K)/PB) I/O complexity, where K is the sum of counts of all the ranges. The key to achieving efficient load balancing among the processors for this problem is a new method to count the output without enumerating it, which might be of independent interest. Keywords-parallel external memory, PEM, multicore algorithms, computational geometry, parallel distribution sweeping