Coding Schemes for Document Exchange under Multiple Substring Edits
Hrishi Narayanan, Vinayak Ramkumar, Rawad Bitar, Antonia Wachter-Zeh

TL;DR
This paper introduces efficient document exchange schemes for binary strings under multiple bounded substring edits, achieving near-optimal encoding lengths with low computational complexity and analyzing average case performance.
Contribution
It presents a low-complexity encoding scheme for multiple substring edits and analyzes average encoding lengths, extending prior work from single to multiple edits.
Findings
Encoding length of 4t log n + o(log n) bits with low complexity.
Average encoding length of (4t - 1) log n + o(log n) for uniform strings.
Prior schemes only addressed single substring edits.
Abstract
We study the document exchange problem under multiple substring edits. A substring edit in a string occurs when a substring of is replaced by an arbitrary string . The lengths of and are bounded from above by a fixed constant. Let and be two binary strings that differ by multiple substring edits. The aim of document exchange schemes is to construct an encoding of with small length such that can be recovered using and the encoding. We construct a low-complexity document exchange scheme with encoding length of bits, where is the length of the string . The best known scheme achieves an encoding length of bits, but at a much higher computational complexity. Then, we investigate the average…
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Taxonomy
TopicsAlgorithms and Data Compression · DNA and Biological Computing · Network Packet Processing and Optimization
