Skew Heaps:Bibliographic Remarks

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Bibliographic Remarks

Skew Heaps were introduced by Sleator and Tarjan [7]. Leftist Trees have O(log n) worst case complexity for all the Meldable Priority Queue operations but they require heights of each subtree to be maintained as additional information at each node. Skew Heaps are simpler than Leftist Trees in the sense that no additional ’balancing’ information need to be maintained and the meld operation simply swaps the children of the right most path without any constraints and this results in a simpler code. The bound 3 log2 n + 2 for melding was significantly improved to logφ n( here φ denotes the well-known golden ratio (√5 + 1)/2 which is roughly 1.6) by using a different potential function and an intricate analysis in [6].

Recently, this bound was shown to be tight in [2]. Pairing Heap, introduced by Fredman et al. [5], is yet another self-adjusting heap structure and its relation to Skew Heaps is explored in Chapter 7 of this handbook.

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