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

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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.