The Violation Heap: A Relaxed Fibonacci-Like Heap

TL;DR

This paper introduces the Violation Heap, a relaxed Fibonacci-like priority queue that matches Fibonacci heaps' amortized bounds while offering simplicity and potentially better practical performance.

Contribution

It presents a new relaxed heap structure that simplifies implementation and maintains optimal amortized bounds similar to Fibonacci heaps.

Findings

Achieves O(1) find-min and insert operations.

Supports O(1) amortized decrease-key.

Provides O(log n) delete-min operation.

Abstract

We give a priority queue that achieves the same amortized bounds as Fibonacci heaps. Namely, find-min requires O(1) worst-case time, insert, meld and decrease-key require O(1) amortized time, and delete-min requires $O(\log n)$ amortized time. Our structure is simple and promises an efficient practical behavior when compared to other known Fibonacci-like heaps. The main idea behind our construction is to propagate rank updates instead of performing cascaded cuts following a decrease-key operation, allowing for a relaxed structure.