Given a set P of n locations on which facilities can be placed and an integer k, we want to place k facilities on some locations so that a designated objective function is maximized. The problem is called the k-dispersion problem. In this paper we give a simple O(n) time algorithm to solve the maxmin version of the k-dispersion problem if P is a set of points on a line. This is the first O(n) time algorithm to solve the max-min k-dispersion problem for the set of "unsorted" points on a line. If P is a set of sorted points on a line, and the input is given as an array in which the coordinates of the points are stored in the sorted order, then by slightly modifying the algorithm above one can solve the dispersion problem in O(log n) time. This is the first sublinear time algorithm to solve the max-min k-dispersion problem for the set of sorted points on a line.
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Univ Hong Kong, Dept Math, Adv Modeling & Appl Comp Lab, Hong Kong, Hong Kong, Peoples R ChinaUniv Hong Kong, Dept Math, Adv Modeling & Appl Comp Lab, Hong Kong, Hong Kong, Peoples R China
Ching, Wai-Ki
Cong, Yang
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Univ Hong Kong, Dept Math, Adv Modeling & Appl Comp Lab, Hong Kong, Hong Kong, Peoples R ChinaUniv Hong Kong, Dept Math, Adv Modeling & Appl Comp Lab, Hong Kong, Hong Kong, Peoples R China
Cong, Yang
Tsing, Nam-Kiu
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Univ Hong Kong, Dept Math, Adv Modeling & Appl Comp Lab, Hong Kong, Hong Kong, Peoples R ChinaUniv Hong Kong, Dept Math, Adv Modeling & Appl Comp Lab, Hong Kong, Hong Kong, Peoples R China
机构:
Univ Ljubljana, Fac Educ, Ljubljana 1000, SloveniaUniv Ljubljana, Fac Educ, Ljubljana 1000, Slovenia
Cencelj, Matija
Repovs, Dusan
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Univ Ljubljana, Fac Educ, Ljubljana 1000, Slovenia
Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, SloveniaUniv Ljubljana, Fac Educ, Ljubljana 1000, Slovenia
Repovs, Dusan
Zarichnyi, Michael
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Lviv Natl Univ, Dept Mech & Math, UA-79000 Lvov, Ukraine
Univ Rzeszow, Inst Math, PL-35310 Rzeszow, PolandUniv Ljubljana, Fac Educ, Ljubljana 1000, Slovenia