File Updates Under Random/Arbitrary Insertions And Deletions

TL;DR

This paper investigates efficient communication methods for updating files after random or arbitrary insertions and deletions, providing theoretical bounds and practical algorithms that are near-optimal in rate.

Contribution

It introduces models for file editing with insertions/deletions, derives lower bounds on update rates, and develops algorithms that approach these bounds.

Findings

Derived information-theoretic lower bounds on update rates.

Developed dynamic programming and entropy coding algorithms.

Achieved near-optimal compression rates for file updates.

Abstract

A client/encoder edits a file, as modeled by an insertion-deletion (InDel) process. An old copy of the file is stored remotely at a data-centre/decoder, and is also available to the client. We consider the problem of throughput- and computationally-efficient communication from the client to the data-centre, to enable the server to update its copy to the newly edited file. We study two models for the source files/edit patterns: the random pre-edit sequence left-to-right random InDel (RPES-LtRRID) process, and the arbitrary pre-edit sequence arbitrary InDel (APES-AID) process. In both models, we consider the regime in which the number of insertions/deletions is a small (but constant) fraction of the original file. For both models we prove information-theoretic lower bounds on the best possible compression rates that enable file updates. Conversely, our compression algorithms use dynamic programming (DP) and entropy coding, and achieve rates that are approximately optimal.