TY - GEN

T1 - The amortized cost of finding the minimum

AU - Kaplan, Haim

AU - Zamir, Or

AU - Zwick, Uri

N1 - Publisher Copyright:
Copyright © 2015 by the Society for Industrial and Applied Mathmatics.

PY - 2015

Y1 - 2015

N2 - We obtain an essentially optimal tradeoff between the amortized cost of the three basic priority queue operations insert, delete and f ind-min in the comparison model. More specifically, we show that A(find-min) = ω(n/(2+ε)(A(insert)+(A(delete)), A(find-min) = ω= O(n/(2+ε)(A(insert)+(A(delete) + log n), for any fixed ε > 0, where n is the number of items in the priority queue and A(insert), A(delete) and A(iind-min) are the amortized costs of the insert, delete and find-min operations, respectively. In particular, if A(insert) + A(delete) = O(1), then A(find-min) = ω(n), and .A(f ind-min) = O(na), for some α < 1, only if A(insert) + A(delete) = ω(log n). (We can, of course, have A(insert) = O(1), A(delete) = O(log n), or vice versa, and A(find-min) = O(1).) Our lower bound holds even if randomization is allowed. Surprisingly, such fundamental bounds on the amortized cost of the operations were not known before. Brodal, Chaudhuri and Rad-hakrishnan, obtained similar bounds for the worst-case complexity of f ind-min.

AB - We obtain an essentially optimal tradeoff between the amortized cost of the three basic priority queue operations insert, delete and f ind-min in the comparison model. More specifically, we show that A(find-min) = ω(n/(2+ε)(A(insert)+(A(delete)), A(find-min) = ω= O(n/(2+ε)(A(insert)+(A(delete) + log n), for any fixed ε > 0, where n is the number of items in the priority queue and A(insert), A(delete) and A(iind-min) are the amortized costs of the insert, delete and find-min operations, respectively. In particular, if A(insert) + A(delete) = O(1), then A(find-min) = ω(n), and .A(f ind-min) = O(na), for some α < 1, only if A(insert) + A(delete) = ω(log n). (We can, of course, have A(insert) = O(1), A(delete) = O(log n), or vice versa, and A(find-min) = O(1).) Our lower bound holds even if randomization is allowed. Surprisingly, such fundamental bounds on the amortized cost of the operations were not known before. Brodal, Chaudhuri and Rad-hakrishnan, obtained similar bounds for the worst-case complexity of f ind-min.

UR - http://www.scopus.com/inward/record.url?scp=84938265293&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973730.51

DO - 10.1137/1.9781611973730.51

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AN - SCOPUS:84938265293

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 757

EP - 768

BT - Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015

PB - Association for Computing Machinery

T2 - 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015

Y2 - 4 January 2015 through 6 January 2015

ER -