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- W3100384259 abstract "In k-Clustering we are given a multiset of n vectors X⊂Zd and a nonnegative number D, and we need to decide whether X can be partitioned into k clusters C1,…,Ck such that the cost∑i=1kminci∈Rd∑x∈Ci‖x−ci‖pp≤D, where ‖⋅‖p is the Lp-norm. For p=2, k-Clustering is k-Means. We study k-Clustering from the perspective of parameterized complexity. The problem is known to be NP-hard for k=2 and also for d=2. It is a long-standing open question, whether the problem is fixed-parameter tractable (FPT) for the combined parameter d+k. In this paper, we focus on the parameterization by D. We complement the known negative results by showing that for p=0 and p=∞, k-Clustering is W[1]-hard when parameterized by D. Interestingly, we discover a tractability island of k-Clustering: for every p∈(0,1], k-Clustering is solvable in time 2O(DlogD)(nd)O(1)." @default.
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- W3100384259 date "2021-05-01" @default.
- W3100384259 modified "2023-10-02" @default.
- W3100384259 title "Parameterized k-Clustering: Tractability island" @default.
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- W3100384259 doi "https://doi.org/10.1016/j.jcss.2020.10.005" @default.
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