Soft Heap

In computer science, a soft heap is a variant on the simple heap data structure that has constant amortized time for 5 types of operations. This is achieved by carefully "corrupting" (increasing) the keys of at most a certain fixed percentage of values in the heap. The constant time operations are:

• create(S): Create a new soft heap
• insert(S, x): Insert an element into a soft heap
• meld(S, S' ): Combine the contents of two soft heaps into one, destroying both
• delete(S, x): Delete an element from a soft heap
• findmin(S): Get the element with minimum key in the soft heap

It was designed by Bernard Chazelle in 2000. The term "corruption" in the structure is the result of what Chazelle called "carpooling" in a soft heap. Each node in the soft heap contains a linked-list of keys and one common key. The common key is an upper bound on the values of the keys in the linked-list. Once a key is added to the linked-list, it is considered corrupted because its value is never again relevant in any of the soft heap operations: only the common keys are compared. It is unpredictable which keys will be corrupted in this manner; it is only known that at most a fixed percentage will be corrupted. This is what makes soft heaps "soft"; you can't be sure whether or not any particular value you put into it will be corrupted. The purpose of these corruptions is effectively to lower the information entropy of the data, enabling the data structure to break through information-theoretic barriers regarding heaps.

Other heaps such as Fibonacci heaps achieve most of these bounds without any corruption, but cannot provide a constant-time bound on the critical delete operation. The percentage of values which are corrupted can be chosen freely, but the lower this is set, the more time insertions require (O(log 1/ε) for an error rate of ε).