| Meldable Heaps and Boolean Union-Find (extended abstract) (2007) | |||||||||||||||
Abstract | |||||||||||||||
| In the classical meldable heap data type we maintain an item-disjoint collection of heaps under the operations ndmin, insert, delete, decrease-key, and meld. In the usual de nition decrease-key and delete get the item and the heap containing it as parameters. We consider the modied problem where decrease-key and delete get only the item but not the heap containing it. We show that for this problem one of the operations nd-min, decrease-key, or meld must take non-constant time. This is in contrast with the original data type in which data structures supporting all these three operations in constant time are known (both in an amortized and a worst-case setting). To establish our results for meldable heaps we consider a weaker version of the union-nd problem that is of independent interest, which we call Boolean union-nd. In the Boolean union-nd problem the nd operation is a binary predicate that gets an item x and a set A and answers positively if and only if x 2 A. We prove that the lower bounds which hold for union-nd in the cell probe model hold for Boolean union-nd as well. We also suggest new heap data structures implementing the modied meldable heap data type that are based on redundant binary counters. Our data structures have good worst-case bounds. The best of our data structures matches the worst-case lower bounds which we establish for the problem. The simplest of our data structures is an interesting generalization of binomial queues. | |||||||||||||||
Details der Publikation | |||||||||||||||
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