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Abstract: Given a set of n real values, each with a positive weight, we wish to find the subset of n - k values having maximum weighted average. This is equivalent to the following form of parametric selection: given n objects with values decreasing linearly with time, find the time at which the n - k maximum values add to zero. We give several algorithms showing that these problems can be solved in time O(n) (independent of k). We also show that a slight generalization of the original ... (Update)
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.... in time O(n) Further details and pseudocode of this deterministic algorithm can be found in the technical report version of this paper [8]. 7 Negative weights The methods we have described do not make any assumption about the values v i , however the non negativity of the...
...can be defined. Linear time algorithms for an analog to (P2) for uniform matroids have been devised by Eppstein and Hirschberg [EpHi95]. Cole s parametric minimum spanning tree algorithm is a clever application of Megiddo s method of parametric search [Meg79, Meg83] a...
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BibTeX entry: (Update)
D. Eppstein and D. S. Hirschberg. Choosing subsets with maximum weighted average. Tech. Rep. 95-12, Dept. Inf. & Comp. Sci., UC Irvine, 1995. http://citeseer.ist.psu.edu/article/eppstein95choosing.html More
@article{ eppstein97choosing,
author = "David Eppstein and Daniel S. Hirschberg",
title = "Choosing Subsets with Maximum Weighted Average",
journal = "J. Algorithms",
volume = "24",
number = "1",
pages = "177-193",
year = "1997",
url = "citeseer.ist.psu.edu/article/eppstein95choosing.html" }
Citations (may not include all citations):773 Reducibility among combinatorial problems (context) - Karp - 1972
185 Applying parallel computation algorithms in the design of se.. (context) - Megiddo - 1983
146 Computers and Intractibility: A Guide to the Theory of NP-Co.. (context) - Garey, Johnson - 1979
102 A characterization of the minimum cycle mean in a digraph (context) - Karp - 1978
95 Linear programming and convex hulls made easy (context) - Seidel - 1990
81 A subexponential bound for linear programming - Matousek, Sharir et al. - 1992
80 Slowing down sorting networks to obtain faster sorting algor.. (context) - Cole - 1984
43 Approximations and optimal geometric divide-and-conquer (context) - Matousek - 1991
42 An optimal-time algorithm for slope selection (context) - Cole, Salowe et al. - 1989
41 Randomized optimal algorithm for slope selection (context) - Matousek - 1991
40 Probabilistic recurrence relations (context) - Karp - 1994
34 A randomized algorithm for slope selection (context) - Dillencourt, Mount et al. - 1992
33 An upper bound on the number of planar k-sets (context) - Pach, Steiger et al. - 1992
29 A Las Vegas algorithm for linear programming when the dimens.. (context) - Clarkson - 1988
24 Finding minimum cost to time ratio cycles with small integra.. (context) - Hartmann, Orlin - 1993
23 Optimal slope selection via expanders - Katz, Sharir - 1993
23 Faster parametric shortest path and minimum-balance algorith.. - Young, Tarjan et al. - 1991
19 A subexponential algorithm for abstract optimization problem.. (context) - Gartner - 1992
18 Parametric shortest path algorithms with an application to c.. (context) - Karp, Orlin - 1981
15 Geometric lower bounds for parametric matroid optimization - Eppstein - 1995
13 Randomizing optimal geometric algorithms (context) - Shafer, Steiger - 1993
10 Helly theorems and generalized linear programming - Amenta - 1993
9 The centroid of points with approximate weights - Bern, Eppstein et al. - 1995
8 Finding minimum-cost circulations by cancelling negative cyc.. (context) - Goldberg, Tarjan - 1989
7 Tight bounds on the number of minimum-mean cycle cancellatio.. (context) - Radzik, Goldberg - 1994
5 Two strongly polynomial cut cancelling algorithms for minimu.. (context) - Ervolina, McCormick - 1993
5 A new scaling algorithm for the maximum mean cut problem (context) - Iwano, Misono et al. - 1994
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Linear Complexity Hexahedral Mesh Generation - Eppstein (1996) (Correct)
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