List Heaps

TL;DR

This paper introduces List Heaps, an adaptive heap structure that improves performance by exploiting input presortedness, with initial empirical evidence and potential for further theoretical study.

Contribution

The paper proposes List Heaps, a simple extension of binary heaps, demonstrating how adaptive heaps can leverage input presortedness to enhance practical performance.

Findings

List Heaps show improved empirical performance on structured inputs.

Adaptive heaps exploit input presortedness for efficiency gains.

Initial tests support the potential of adaptive heaps in practical applications.

Abstract

This paper presents a simple extension of the binary heap, the List Heap. We use List Heaps to demonstrate the idea of adaptive heaps: heaps whose performance is a function of both the size of the problem instance and the disorder of the problem instance. We focus on the presortedness of the input sequence as a measure of disorder for the problem instance. A number of practical applications that rely on heaps deal with input that is not random. Even random input contains presorted subsequences. Devising heaps that exploit this structure may provide a means for improving practical performance. We present some basic empirical tests to support this claim. Additionally, adaptive heaps may provide an interesting direction for theoretical investigation.