2013/02/26 by John Iacono, Iacono, John · 1 citation
Computer Science · #Algorithms and Data Compression #Data Structures and Algorithms (cs.DS) #E.1 #FOS: Computer and information sciences #Natural Language Processing Techniques #Network Packet Processing and Optimization #Software Testing and Debugging Techniques #cs.DS
paper · pdf · doi:10.48550/arxiv.1302.6641
openalex publication_date 2013/02/26 · arxiv created 2013/07/16 · arxiv updated 2013/07/17 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
A lower bound is presented which shows that a class of heap algorithms in the pointer model with only heap pointers must spend Omega(log log n / log log log n) amortized time on the decrease-key operation (given O(log n) amortized-time extract-min). Intuitively, this bound shows the key to having O(1)-time decrease-key is the ability to sort O(log n) items in O(log n) time; Fibonacci heaps [M.L. Fredman and R. E. Tarjan. J. ACM 34(3):596-615 (1987)] do this through the use of bucket sort. Our lower bound also holds no matter how much data is augmented; this is in contrast to the lower bound of Fredman [J. ACM 46(4):473-501 (1999)] who showed a tradeoff between the number of augmented bits and the amortized cost of decrease-key. A new heap data structure, the sort heap, is presented. This heap is a simplification of the heap of Elmasry [SODA 2009: 471-476] and shares with it a O(log log n) amortized-time decrease-key, but with a straightforward implementation such that our lower bound holds. Thus a natural model is presented for a pointer-based heap such that the amortized runtime of a self-adjusting structure and amortized lower asymptotic bounds for decrease-key differ by but a O(log log log n) factor.