一类一维在线单位聚类问题的随机近似算法

doi:10.15960/j.cnki.issn.1007-6093.2022.03.011

Abstract

Abstract:

In a given metric space, the unit clustering problem is to find a minimum number of unit balls to cover all the given points. It is a well known combinatorial optimization problem and the online version is: Given a set of n points in a given metric space, which arrive one by one at any locations, the point should be assigned to a unit cluster at the time of its arrival without any future information, the goal is to minimize the number of used clusters. In this paper, we consider a class of online unit clustering problem in one dimension with the assumption that the distance between any two adjacent clusters in the offline optimal solution is greater than 0.5. We first present two online algorithms with some lemmas, and then present a combined randomized algorithm which run the two online algorithms with a probability 0.5. We show that the expected competitive ratio of the combined randomized algorithm is at most 1.5.

Key words: unit clustering problem, online algorithm, randomized algorithm, competitive ratio

CLC Number:

O224

Yubo DAI, Yihong DUAN, Longcheng LIU, Zihao WANG. Randomized approximation algorithms for a class of one-dimensional online unit clustering problem[J]. Operations Research Transactions, 2022, 26(3): 143-150.

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Randomized approximation algorithms for a class of one-dimensional online unit clustering problem

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