TY - GEN

T1 - DecreaseKeys are expensive for external memory priority queues

AU - Eenberg, Kasper

AU - Larsen, Kasper Green

AU - Yu, Huacheng

N1 - Publisher Copyright:
© 2017 ACM.

PY - 2017/6/19

Y1 - 2017/6/19

N2 - One of the biggest open problems in external memory data structures is the priority queue problem with DecreaseKey operations. If only Insert and ExtractMin operations need to be supported, one can design a comparison-based priority queue performing O((N/B) lgM/B N) I/Os over a sequence of N operations, where B is the disk block size in number of words and M is the main memory size in number of words. This matches the lower bound for comparison-based sorting and is hence optimal for comparison-based priority queues. However, if we also need to support DecreaseKeys, the performance of the best known priority queue is only O((N/B) lg2 N) I/Os. The big open question is whether a degradation in performance really is necessary. We answer this question affirmatively by proving a lower bound of Ω((N/B) lglgN B) I/Os for processing a sequence of N intermixed Insert, ExtraxtMin and DecreaseKey operations. Our lower bound is proved in the cell probe model and thus holds also for non-comparison-based priority queues.

AB - One of the biggest open problems in external memory data structures is the priority queue problem with DecreaseKey operations. If only Insert and ExtractMin operations need to be supported, one can design a comparison-based priority queue performing O((N/B) lgM/B N) I/Os over a sequence of N operations, where B is the disk block size in number of words and M is the main memory size in number of words. This matches the lower bound for comparison-based sorting and is hence optimal for comparison-based priority queues. However, if we also need to support DecreaseKeys, the performance of the best known priority queue is only O((N/B) lg2 N) I/Os. The big open question is whether a degradation in performance really is necessary. We answer this question affirmatively by proving a lower bound of Ω((N/B) lglgN B) I/Os for processing a sequence of N intermixed Insert, ExtraxtMin and DecreaseKey operations. Our lower bound is proved in the cell probe model and thus holds also for non-comparison-based priority queues.

KW - Communication complexity

KW - External memory

KW - Lower bound

KW - Priority queues

UR - http://www.scopus.com/inward/record.url?scp=85024391830&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85024391830&partnerID=8YFLogxK

U2 - 10.1145/3055399.3055437

DO - 10.1145/3055399.3055437

M3 - Conference contribution

AN - SCOPUS:85024391830

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1081

EP - 1093

BT - STOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

A2 - McKenzie, Pierre

A2 - King, Valerie

A2 - Hatami, Hamed

PB - Association for Computing Machinery

T2 - 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017

Y2 - 19 June 2017 through 23 June 2017

ER -