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- W2469837900 abstract "Let V be a set of n points in R d , which we call voters. A point p ∈ R d is preferred over another point p ′ ∈ R d by a voter υ ∈ V if dist(υ, p ) < dist(υ, p ′). A point p is called a plurality point if it is preferred by at least as many voters as any other point p ′. We present an algorithm that decides in O ( n log n ) time whether V admits a plurality point in the L 2 norm and, if so, finds the (unique) plurality point. We also give efficient algorithms to compute a minimum-cost subset W ⊂ V such that V W admits a plurality point, and to compute a so-called minimum-radius plurality ball. Finally, we consider the problem in the personalized L 1 norm, where each point υ ∈ V has a preference vector 〈 w 1 (υ),…, w d (υ)〉 and the distance from υ to any point p ∈ R d is given by ∑ i =1 d w i (υ)· | x i (υ)− x i ( p )|. For this case we can compute in O ( n d −1 ) time the set of all plurality points of V . When all preference vectors are equal, the running time improves to O ( n )." @default.
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- W2469837900 date "2018-06-16" @default.
- W2469837900 modified "2023-09-26" @default.
- W2469837900 title "Faster Algorithms for Computing Plurality Points" @default.
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- W2469837900 doi "https://doi.org/10.1145/3186990" @default.
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