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Improved selection in totally monotone arrays
Y. Mansour, J.K. Park, B. Schieber,
Published in Springer Verlag
Volume: 560 LNCS
Pages: 347 - 359
This paper’s main result is an O((√m lg m)(n lg n)+m lg n)-time algorithm for computing the kth smallest entry in each row of an m × n totally monotone array. (A two-dimensional array A = {a[i,j]} is totally monotone if for all i1 < i2 and j1 < j2, a[i1,j1] < a[i1, j2] implies a[i2, j1] < a[i2, j2].) For large values of k (in particular, for k = n/2'|), this algorithm is significantly faster than the O(k(m + n))-time algorithm for the same problem due to Kravets and Park (1991). An immediate consequence of this result is an O(n3/2 lg2 n)-time algorithm for computing the kth nearest neighbor of each vertex of a convex n-gon. In addition to the main result, we also give an O(n lg m)-time algorithm for computing an approximate median in each row of an m × n totally monotone array; this approximate median is an entry whose rank in its row lies between [n/4] and [3n/4]. © Springer-Verlag Berlin Heidelberg 1991.
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