Applications of matching theory in constraint programming

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Two-tier relaxed heaps

Abstract. We introduce an adaptation of run-relaxed heaps which provides efficient heap operations with respect to the number of element comparisons performed. Our data structure guarantees the worst-case cost of O(1) for find-min, insert, and decrease; and the worst-case cost of O(lg n) with at most lg n + 3 lg lg n + O(1) element comparisons for delete, improving the bound of 3lg n + O(1) on the number of element comparisons known for run-relaxed heaps. Here, n denotes the number of elements stored prior to the operation in question, and lg n equals max {1, log 2 n}.