Rank-Relaxed Weak Queues: Faster than Pairing and Fibonacci Heaps?

A run-relaxed weak queue by Elmasry et al. (2005) is a priority queue data structure with insert and decrease-key in O(1) as well as delete and delete-min in O(log n) worst-case time. One further advantage is the small space consumption of 3n+O(log n) pointers. In this paper we propose rank-relaxed weak queues, reducing the number of rank violations nodes for each level to a constant, while providing amortized constant time for decrease-key. Compared to runrelaxed weak queues, the new structure additionally gains one pointer per node. An empirical evaluation shows that the implementation can outperform Fibonacci and pairing heaps in practice even on rather simple data types.