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Efficient Computation of the Maximum of the Sum of Two Sequences and Applications

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1 Author(s)
Konard, V. ; Hewlett-Packard

Computing max{a1+ b1, a2+ b2, ... ,an+ bn} trivially takes n additions. We show that if we are given the ranking for the a's and the b's separately, then an algorithm exists which will compute the maximum in ≅2n additions on the average. This can be generalized to yield an efficient algorithm to compute max{h(a1,b1), h(a2,b2),..., h(an, bn)} where h(x,y) is monotone increasing in x and y. Another generalization shows an efficient way of computing the maximum norm of a difference between two vectors. Applications are shown in pattern classification and computational geometry.

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Computers, IEEE Transactions on  (Volume:C-35 ,  Issue: 7 )