Searching Lattice Data Structures of Varying Degrees of Sortedness

TL;DR

This paper introduces a jump searching algorithm for lattice data structures with varying sortedness, along with a sorting method to improve their efficiency during idle system times.

Contribution

It presents a novel jump searching algorithm with complexity depending on lattice sortedness and a sorting procedure to enhance lattice sortedness during idle times.

Findings

Jump search complexity is $O(J(L)\log(N))$, with $J(L)$ approaching 4 for highly sorted lattices.

A sorting procedure with $O(\sqrt{N})$ complexity improves lattice sortedness during idle system time.

Lattice data structures are shown to be space-efficient and cache-suitable.

Abstract

Lattice data structures are space efficient and cache-suitable data structures. The basic searching, insertion, and deletion operations are of time complexity $O(\sqrt{N})$. We give a jump searching algorithm of time complexity $O(J(L)\log(N))$, where $J(L)$ is the jump factor of the lattice. $J(L)$ approaches $4$ when the degree of sortedness of the lattice approaches $\sqrt{N}$. A sorting procedure of time complexity $O(\sqrt{N})$ that can be used, during the system idle time, to increase the degree of sortedness of the lattice is given.