Characterization of Request Sequences for List Accessing Problem and New Theoretical Results for MTF Algorithm

TL;DR

This paper characterizes request sequences in the list accessing problem, focusing on factors like size and frequency, and provides new theoretical insights into the Move-To-Front algorithm for these sequences.

Contribution

It introduces a novel characterization of request sequences for the list accessing problem and presents new theoretical results for the MTF algorithm based on this characterization.

Findings

Characterized request sequences based on size, order, and frequency.

Derived new theoretical results for MTF algorithm on these sequences.

Opened new research directions for empirical analysis of list accessing algorithms.

Abstract

List Accessing Problem is a well studied research problem in the context of linear search. Input to the list accessing problem is an unsorted linear list of distinct elements along with a sequence of requests, where each request is an access operation on an element of the list. A list accessing algorithm reorganizes the list while processing a request sequence on the list in order to minimize the access cost. Move-To-Front algorithm has been proved to be the best performing list accessing online algorithm till date in the literature. Characterization of the input request sequences corresponding to practical real life situations is a big challenge for the list accessing problem. As far as our knowledge is concerned, no characterization for the request sequences has been done in the literature till date for the list accessing problem. In this paper, we have characterized the request sequences for the list accessing problem based on several factors such as size of the list, size of the request sequence, ordering of elements and frequency of occurrence of elements in the request sequence. We have made a comprehensive study of MTF list accessing algorithm and obtained new theoretical results for our characterized special class of request sequences. Our characterization will open up a new direction of research for empirical analysis of list accessing algorithms for real life inputs.