Abstract
Consider a setF ofn functions defined on a common intervalU. A ranked function overF is defined from the functions ofF by using order information such as thek largest function, the sum ofk largest functions, etc. We give a linear time randomizing algorithmic paradigm for finding local roots, optima, intersection points, etc., of ranked functions. The algorithm is generalized to the Cost Effective Resource Allocation Problem and to various variants of the Parametric Knapsack Problem.
Similar content being viewed by others
References
M. E. Dyer, On a multidimensional search technique and its application to the Euclidean one center problem, Department of Mathematics, Teesside Polytechnic, 1984.
N. Megiddo, An application of parallel computation to sequential computation: The problem of cost effective resource allocation, TWISK 202 CSIR-NRIMS, Pretoria, S. Africa, 1981.
N. Megiddo, Applying parallel computation algorithms in the design of serial algorithms,J. Assoc. Comput. Mech.,30 (1983), 852–865.
N. Megiddo, The weighted Euclidean one center problem,Math. Oper. Res.,8 (1983), 498–505.
N. Megiddo and E. Zemel, AnO(n logn) randomized algorithm for the weighted Euclidean one center problem,Algorithmica (to appear).
M. O. Rabin, Probabilistic algorithms, in Algorithms and Complexity: New Directions and Recent Results (J. F. Traub, ed.), Academic Press, New York, 1976.
R. Reischuk, A fast probabilistic parallel sorting algorithm,22nd Annual Symposium on Foundation of Computer Sciences, 1981, pp. 212–219.
E. Zemel, A parallel randomized algorithm for selection with applications, Working Paper No. 761/82, Israel Institute for Business Research, Tel Aviv University, November 1982.
Author information
Authors and Affiliations
Additional information
Communicated by D. T. Lee.
Part of this work was done when the author was visiting Tel Aviv University.
Supported, in part, by NSF Grant ECS-812141, and by the Mia Fischer David Foundation through the Israel Institute of Business Research, Tel Aviv University. IIBR working papers are intended for preliminary circulation of tentative research results. Comments are welcome and should be addressed directly to the author.
Rights and permissions
About this article
Cite this article
Zemel, E. A linear time randomizing algorithm for searching ranked functions. Algorithmica 2, 81–90 (1987). https://doi.org/10.1007/BF01840350
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01840350