A simple greedy approximation algorithm for the minimum connected $$k$$ k -Center problem

Dongyue Liang, Liquan Mei, James Willson and Wei Wang ()
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Dongyue Liang: Xi’an Jiaotong University
Liquan Mei: Xi’an Jiaotong University
James Willson: University of Texas at Dallas
Wei Wang: Xi’an Jiaotong University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 4, No 5, 1417-1429

Abstract: Abstract In this paper, we consider the connected $$k$$ k -Center ( $$CkC$$ C k C ) problem, which can be seen as the classic $$k$$ k -Center problem with the constraint of internal connectedness, i.e., two nodes in a cluster are required to be connected by an internal path in the same cluster. $$CkC$$ C k C was first introduced by Ge et al. (ACM Trans Knowl Discov Data 2:7, 2008), in which they showed the $$NP$$ N P -completeness for this problem and claimed a polynomial time approximation algorithm for it. However, the running time of their algorithm might not be polynomial, as one key step of their algorithm involves the computation of an $$NP$$ N P -hard problem. We first present a simple polynomial time greedy-based $$2$$ 2 -approximation algorithm for the relaxation of $$CkC$$ C k C —the $$CkC^*$$ C k C ∗ . Further, we give a $$6$$ 6 -approximation algorithm for $$CkC$$ C k C .

Keywords: k-Center; Greedy algorithm; Approximation algorithm (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-015-9831-8

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