Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
Parallel searching in generalized Monge arrays with applications
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Optimal routing of parentheses on the hypercube
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
A unifying look at data structures
Communications of the ACM
Optimal Algorithms on the Pipelined Hypercube and Related Networks
IEEE Transactions on Parallel and Distributed Systems
Average-Case Communication-Optimal Parallel Parenthesis Matching
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Efficient Parallel Tree Reductions on Distributed Memory Environments
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
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Given a sequence of n elements, the All Nearest Smaller Values (ANSV) problem is to find, for each element in the sequence, the nearest element to the left (right) that is smaller, or to report that no such element exists. Time and work optimal algorithms for this problem are known on all the PRAM models [3], [5] but the running time of the best previous hypercube algorithm [6] is optimal only when the number of processors p satisfies 1 驴p驴n/((lg3n)(lg lg n)2). In this paper, we prove that any normal hypercube algorithm requires 驴(n) processors to solve the ANSV problem in O(lg n) time, and we present the first normal hypercube ANSV algorithm that is optimal for all values of n and p. We use our ANSV algorithm to give the first O(lg n)-time n-processor normal hypercube algorithms for triangulating a monotone polygon and for constructing a Cartesian tree.