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Given a sequence of n real numbers A = a1, a2,. .. , an and a positive integer k, the Sum Selection Problem is to find the segment A(i, j) = ai, ai+1,. .. , aj such that the rank of the sum s(i, j) = È j t=i at is k over all n(n−1) 2 segments. We present a deterministic algorithm for this problem that runs in O(n log n) time. The previously best known… (More)

A prototype is representative of a set of similar objects. This paper proposes an approach that formulates the problem of prototype generation as finding the mean from a given set of objects, where the prototype solution must satisfy certain constraints. These constraints describe the important perceptual features of the sample shapes that the proposed… (More)

In 1982, Drezner proposed the (1|1)-centroid problem on the plane, in which two players, called the leader and the follower, open facilities to provide service to customers in a competitive manner. The leader opens the first facility, and the follower opens the second. Each customer will patronize the facility closest to him (ties broken in favor of the… (More)

- Ansgar Grüne, Tien-Ching Lin, Teng-Kai Yu, Rolf Klein, Elmar Langetepe, Der-Tsai Lee +1 other
- ISAAC
- 2010

The spanning ratio and maximum detour of a graph G embedded in a metric space measure how well G approximates the minimum complete graph containing G and metric space, respectively. In this paper we show that computing the spanning ratio of a rectilinear path P in L 1 space has a lower bound of Ω(n log n) in the algebraic computation tree model and describe… (More)