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Title: Improved selection in totally monotone arrays

Conference ·
OSTI ID:5241353
 [1];  [2];  [3];  [4]
  1. Harvard Univ., Cambridge, MA (United States). Aiken Computation Lab.
  2. Sandia National Labs., Albuquerque, NM (United States)
  3. International Business Machines Corp., Yorktown Heights, NY (United States). Thomas J. Watson Research Center
  4. AT and T Bell Labs., Murray Hill, NJ (United States)

This paper's main result is an O(({radical}{bar m}lgm)(n lg n) + mlg n)-time algorithm for computing the kth smallest entry in each row of an m {times} n totally monotone array. (A two-dimensional A = a(i,j) is totally monotone if for all i{sub 1} < i{sub 2} and j{sub 1} < j{sup 2}, < a(i{sub 1},j{sub 2}) implies a(i{sub 2},j{sub 1})). 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. An immediate consequence of this result is an O(n{sup 3/2} lg{sup 2}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 {times} n totally monotone array; this approximate median is an entry whose rank in its row lies between (n/4) and (3n/4) {minus} 1. 20 refs., 3 figs.

Research Organization:
Sandia National Labs., Albuquerque, NM (United States)
Sponsoring Organization:
USDOE; USDOE, Washington, DC (United States)
DOE Contract Number:
Report Number(s):
SAND-91-2039C; CONF-911257-1; ON: DE92000817
Resource Relation:
Conference: 11. Foundations of software technology and theoretical computer science, New Dehli (India), 17-19 Dec 1991
Country of Publication:
United States