Optimizing Binary Heaps

Strengthened Lazy Heaps: Surpassing the Lower Bounds for Binary Heaps

Let n denote the number of elements currently in a data structure. An in-place heap is stored in the first n locations of an array, uses O(1) extra space, and supports the operations: minimum , insert , and extract -min. We introduce an in-place heap, for which minimum and insert take O(1) worst-case time, and extract -min takes O(lg n) worst-case time and involves at most lg n+O(1) element com...

Optimizing Memory Management with Object-Local Heaps

Binary Heaps Formally Verified in Why3

The VACID-0 benchmarks is a set of small programs which pose challenges for formal verification of their functional behavior. This paper reports on the formal verification of one of these challenges: binary heaps. The solution given here is performed using the Why3 environment for program verification. The expected behavior of the program is specified in Why3 logic, structured using the constru...

A Functional Approach to Standard Binary Heaps

This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst logarithmic running time for them. Approaches and ideas described in this paper present a simple and asymptotically optimal implementation of immutable binary heap.

Binomial Heaps and Skew Binomial Heaps

We implement and prove correct binomial heaps and skew binomial heaps. Both are data-structures for priority queues. While binomial heaps have logarithmic findMin, deleteMin, insert, and meld operations, skew binomial heaps have constant time findMin, insert, and meld operations, and only the deleteMin-operation is logarithmic. This is achieved by using skew links to avoid cascading linking on ...