Available Stabilizing Heaps

TL;DR

This paper introduces a heap data structure that can recover from illegitimate states after a bounded number of operations, maintaining consistent responses and efficient operation times.

Contribution

It presents a heap construction supporting insert and delete operations in illegitimate states with guaranteed recovery to legitimate states after O(m) steps.

Findings

Supports illegitimate heap states with O(lg K) time per operation

Recovers to legitimate state after O(m) operations

Maintains consistent operation responses during illegitimate states

Abstract

This paper describes a heap construction that supports insert and delete operations in arbitrary (possibly illegitimate) states. After any sequence of at most O(m) heap operations, the heap state is guarantee to be legitimate, where m is the initial number of items in the heap. The response from each operation is consistent with its effect on the data structure, even for illegitimate states. The time complexity of each operation is O(lg K) where K is the capacity of the data structure; when the heap's state is legitimate the time complexity is O(lg n) for n equal to the number items in the heap.