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'''Beap''', or '''bi-parental [[Heap (data_structure)|heap]]''', is a [[data structure]] where a node usually has two parents (unless it is the first or last on a level) and two children (unless it is on the last level). Unlike a heap, a beap allows [[sublinear]] search. The beap was introduced by Ian Munro and Hendra Suwanda. A related data structure is the [[Young tableau]].
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[[Image:beap.jpg|frame|Beap]]
 
==Performance==
 
The height of the structure is approximately <math>\sqrt{n}</math>. Also, assuming the last level is full, the number of elements on that level is also <math>\sqrt{n}</math>. In fact, because of these properties all basic operations (insert, remove, find) run in <math>O(\sqrt{n})</math> time on average. Find operations in the heap can be <math>O(n)</math> in the worst case. Removal and insertion of new elements involves propagation of elements up or down (much like in a heap) in order to restore the beap invariant. An additional perk is that beap provides constant time access to the smallest element and <math>O(\sqrt{n})</math> time for the maximum element.
 
Actually, a <math>O(\sqrt{n})</math> find operation can be implemented if parent pointers at each node are maintained. You would start at the absolute bottom-most element of the top node (similar to the left-most child in a heap) and move either up or right to find the element of interest.
 
==References==
 
J. Ian Munro and Hendra Suwanda. "Implicit data structures for fast search and update". ''[[Journal of Computer and System Sciences]]'', 21(2):236250, 1980.
 
J.W.J Williams in Algorithms 232, "Heapsort", ''[[Comm. ACM 7]]'' (June 1964), 347-348
 
[[Category:Heaps (data structures)]]

Latest revision as of 18:06, 28 April 2014

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