On Lossy Compression of Directed Graphs

Ronit Bustin, Ofer Shayevitz

Research output: Contribution to journalArticlepeer-review

Abstract

The method of types presented by Csiszár and Körner is a central tool used to develop and analyze the basic properties and constraints on sequences of data over finite alphabets. A central problem considered using these tools is that of data compression, and specifically lossy data compression. In this work we consider this very problem, however, instead of sequences of data we consider directed graphs. We show that given a more natural distortion measure, fitting the data structure of a directed graph, the method of types cannot be applied. The suggested distortion measure aims to preserves the local structure of a directed graph. We build on the recent work of Barvinok and extend the method of types to the two dimensional setting of directed graphs. We see that the extension is quite natural in many ways. Given this extension we provide a lower and upper bound on the rate-distortion problem of lossy compression given the suggested distortion measure.

Original languageEnglish
Pages (from-to)2101-2122
Number of pages22
JournalIEEE Transactions on Information Theory
Volume68
Issue number4
DOIs
StatePublished - 1 Apr 2022

Keywords

  • Lossy compression
  • graph theory
  • method-of-types
  • rate-distortion
  • zero-one matrices

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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