Parallel Minimax Searching Algorithm for Extremum of Unimodal Unbounded Function
Boris S. Verkhovsky
DOI: 10.4236/ijcns.2011.49066   PDF   HTML     4,151 Downloads   8,594 Views  


In this paper we consider a parallel algorithm that detects the maximizer of unimodal function f(x) computable at every point on unbounded interval (0, ∞). The algorithm consists of two modes: scanning and detecting. Search diagrams are introduced as a way to describe parallel searching algorithms on unbounded intervals. Dynamic programming equations, combined with a series of liner programming problems, describe relations between results for every pair of successive evaluations of function f in parallel. Properties of optimal search strategies are derived from these equations. The worst-case complexity analysis shows that, if the maximizer is located on a priori unknown interval (n-1], then it can be detected after cp(n)=「2logp/2」+1(n+1)」-1 parallel evaluations of f(x), where p is the number of processors.

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B. Verkhovsky, "Parallel Minimax Searching Algorithm for Extremum of Unimodal Unbounded Function," International Journal of Communications, Network and System Sciences, Vol. 4 No. 9, 2011, pp. 549-561. doi: 10.4236/ijcns.2011.49066.

Conflicts of Interest

The authors declare no conflicts of interest.


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