On the average number of maxima in a set of vectors and applications (1978)
| Venue: | J. ACM |
| Citations: | 73 - 1 self |
BibTeX
@ARTICLE{Bentley78onthe,
author = {J. L. Bentley and H. T. Kung and Carnegie-mellon Umversuy Putsburgh and M. Schkolnick and C. D. Thompson},
title = {On the average number of maxima in a set of vectors and applications},
journal = {J. ACM},
year = {1978},
volume = {25},
pages = {536--543}
}
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Abstract
ABSTRACT. A maximal vector of a set ~s one which is not less than any other vector m all components We derive a recurrence relation for computing the average number of maxunal vectors m a set of n vectors m d-space under the assumpUon that all (nl) a relative ordermgs are equally probable. Solving the recurrence shows that the average number of maxmaa is O((ln n) a-~) for fixed d We use this result to construct an algorithm for finding all the maxima that have expected running tmae hnear m n (for sets of vectors drawn under our assumptions) We then use the result to find an upper bound on the expected number of convex hull points m a random point set KE ~ WORDS AND eHRASES maxtma of a set of vectors, average number of maxtma, expected-tsme algorithms, analysts of algorithms, convex hulls, dynamtc programming CR CATEGORIES " 5 25, 5.39, 5.42 1.
Citations
| 141 | On finding the maxima of a set of vectors - Kung, Luccio, et al. - 1975 |
| 26 | A clustering algorithm for hierarchical structures - SCHKOLNICK - 1977 |
| 10 | On finding the maximal elements in a set of plane vectors - Yao - 1974 |
| 1 | I Divide and conquer for linear expected time lnform Processing Letters 7 - BENTLEY, SHAMOS |
| 1 | E TheArt of Computer Programming, Vol 1 FundamentalAlgonthms - KNUTH - 1973 |
| 1 | A Efficient algonthrns for the partmonmg of trees - s - 1974 |
| 1 | E An algonthm for nonlmear knapsack problems - MORIN, MARSTEN - 1976 |
| 1 | A Encyclopedia of Mathematics and - SANTALO - 1976 |
| 1 | D A clustermg strategy for relational data bases - SCHKOLNICK, THOMPSON - 1977 |
