Traditional data structure designs, whether lock-based or lock-free, provide parallelism via fine grained synchronization among threads. We introduce a new synchronization paradigm based on coarse locking, which we call flat combining. The cost of synchronization in flat combining is so low, that having a single thread holding a lock perform the combined access requests of all others, delivers, up to a certain non-negligible concurrency level, better performance than the most effective parallel finely synchronized implementations. We use flat-combining to devise, among other structures, new linearizable stack, queue, and priority queue algorithms that greatly outperform all prior algorithms.

We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a Davenport-Schinzel sequence S, none of whose subsequences are isomorphic to fixed forbidden subsequence. We direct this technique towards Tarjan’s deque conjecture and prove that n deque operations require O(nα ∗ (n)) time, where α ∗ (n) is the minimum number of applications of the inverse-Ackermann function mapping n to a constant. We are optimistic that this approach could be directed towards other open conjectures on splay trees such as the traversal and split conjectures.

We give a variation of the pairing heaps for which the time bounds for all the operations match the lower bound proved by Fredman for a family of similar self-adjusting heaps. Namely, our heap structure requires O(1) for insert and findmin, O(log n) for delete-min, and O(log log n) for decreasekey and meld (all the bounds are in the amortized sense except for find-min). 1

The Fibonacci heap was devised to provide an especially efficient implementation of Dijkstra’s shortest path algorithm. Although asyptotically efficient, it is not as fast in practice as other heap implementations. Expanding on ideas of Høyer, we describe three heap implementations (two versions of thin heaps and one of thick heaps) that have the same amortized efficiency as Fibonacci heaps but need less space and promise better practical performance. As part of our development, we fill in a gap in Høyer’s analysis.

We study the impact of using different priority queues in the performance of Dijkstra’s SSSP algorithm. We consider only general priority queues that can handle any type of keys (integer, floating point, etc.); the only exception is that we use as a benchmark the DIMACS Challenge SSSP code [1] which can handle only integer values for distances. Our experiments were focussed on the following: 1. We study the performance of two variants of Dijkstra’s algorithm: the well-known version that uses a priority queue that supports the Decrease-Key operation, and another that uses a basic priority queue that supports only Insert and Delete-Min. For the latter type of priority queue we include several for which high-performance code is available such as bottom-up binary heap, aligned 4-ary heap, and sequence heap [33]. 2. We study the performance of Dijkstra’s algorithm designed for flat memory relative to versions that try to be cache-efficient. For this, in main part, we study the difference in performance of Dijkstra’s algorithm relative to the cache-efficiency of the priority queue used, both in-core and out-of-core. We also study the performance of an implementation

Abstract. We introduce the rank-pairing heap, a heap (priority queue) implementation that combines the asymptotic efficiency of Fibonacci heaps with much of the simplicity of pairing heaps. Unlike all other heap implementations that match the bounds of Fibonacci heaps, our structure needs only one cut and no other structural changes per key decrease; the trees representing the heap can evolve to have arbitrary structure. Our initial experiments indicate that rankpairing heaps perform almost as well as pairing heaps on typical input sequences and better on worst-case sequences. 1

Wepresentthefirstpointer-basedheapimplementationwith time bounds matching those of Fibonacci heaps in the worst case. We support make-heap, insert, find-min, meld and decrease-key in worst-case O(1) time, and delete and deletemin in worst-case O(lgn) time, where n is the size of the heap. The data structure uses linear space. A previous, very complicated, solution achieving the same time bounds in the RAM model made essential use of arrays and extensive use of redundant counter schemes to maintain balance. Our solution uses neither. Our key simplification is to discard the structure of the smaller heap when doing a meld. We use the pigeonhole principle in place of the redundant counter mechanism.

Improving the structure and analysis in [1], we give a variation of the pairing heaps that has amortized zero cost per meld (compared to an O(log log n) in [1]) and the same amortized bounds for all other operations. More precisely, the new pairing heap requires: no cost per meld, O(1) per find-min and insert, O(log n) per delete-min, and O(log log n) per decrease-key. These bounds are the best known for any self-adjusting heap, and match the lower bound proven by Fredman for a family of such heaps. Moreover, our structure is even simpler than that in [1]. 1