We present an O(n) algorithm for the linear Multiple Choice Knapsack Problem and its d-dimensional generalization which is based on Megiddo's (1982) algorithm for linear programming. We also consider a certain typ...
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We present an O(n) algorithm for the linear Multiple Choice Knapsack Problem and its d-dimensional generalization which is based on Megiddo's (1982) algorithm for linear programming. We also consider a certain type of convex programming problems which are common in geometric location models. An application of the linear case is an O(n) algorithm for finding a least distance hyperplane in R d according to the rectilinear norm. The best previously available algorithm for this problem was an O(n log 2 n) algorithm for the two-dimensional case. A simple application of the nonlinear case is an O(n) algorithm for finding the point at which a ‘pursuer’ minimizes its distance from the furthest among n ‘targets’, when the trajectories involved are straight lines in R d .
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