TY - JOUR

T1 - An optimal algorithm for finding all the jumps of a monotone step-function

AU - Hassin, Refael

AU - Megiddo, Nimrod

N1 - Funding Information:
San Jose, Calif. 95193. The work Science Foundation Grants ECS-8121741

PY - 1985/6

Y1 - 1985/6

N2 - The idea of binary search is generalized as follows. Given f{hook}: {0, 1,..., N} → {0,..., K} such that f{hook}(0) = 0, f{hook}(N) = K, and f{hook}(i) ≤ f{hook}(j) for i < j, all the "jumps" of f, i.e., all is such that f{hook}(i) > f{hook}(i - 1) together with the difference f{hook}(i) - f{hook}(i - 1) are recognized within K[log2( N K)] + [(N - 1)2-[log2( N K)]]f-evaluations. This is proved to be the exact bound in the non-trivial case when K ≤ N. An optimal strategy is as follows: The first query will be at i = 2m, where m = [log2( N K)]. An adversary will then respond either f{hook}(i) = 0 or f{hook}(i) - 1 as explained in the paper.

AB - The idea of binary search is generalized as follows. Given f{hook}: {0, 1,..., N} → {0,..., K} such that f{hook}(0) = 0, f{hook}(N) = K, and f{hook}(i) ≤ f{hook}(j) for i < j, all the "jumps" of f, i.e., all is such that f{hook}(i) > f{hook}(i - 1) together with the difference f{hook}(i) - f{hook}(i - 1) are recognized within K[log2( N K)] + [(N - 1)2-[log2( N K)]]f-evaluations. This is proved to be the exact bound in the non-trivial case when K ≤ N. An optimal strategy is as follows: The first query will be at i = 2m, where m = [log2( N K)]. An adversary will then respond either f{hook}(i) = 0 or f{hook}(i) - 1 as explained in the paper.

UR - http://www.scopus.com/inward/record.url?scp=0013446487&partnerID=8YFLogxK

U2 - 10.1016/0196-6774(85)90043-4

DO - 10.1016/0196-6774(85)90043-4

M3 - מאמר

AN - SCOPUS:0013446487

VL - 6

SP - 265

EP - 274

JO - Journal of Algorithms

JF - Journal of Algorithms

SN - 0196-6774

IS - 2

ER -