Theory of trinomial heaps

Abstract

We design a new data structure, called a trinomial heap, which supports a decrease-key in O(1) time, and an insert operation and delete-min operation in O(log n) time, both in the worst case, where n is the size of the heap. The merit of the trinomial heap is that it is con-ceptually simpler and easier to implement than the previously invented relaxed heap. The relaxed heap is based on binary linking, while the trinomial heap is based on ternary linking.