Subgraph domatic problem and writing capacity of memory devices with restricted state transitions

Tadashi Wadayama, Taisuke Izumi, Hirotaka Ono

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

A code design problem for memory devices with restricted state transitions is formulated as a combinatorial optimization problem that is called a subgraph domatic partition (subDP) problem. If any neighbor set of a given state transition graph contains all the colors, then the coloring is said to be valid. The goal of a subDP problem is to find the valid coloring that has the largest number of colors for a subgraph of a given directed graph. The number of colors in an optimal valid coloring indicates the writing capacity of that state transition graph. The subDP problems are computationally hard; it is proved to be NP-complete in this paper. One of our main contributions in this paper is to show the asymptotic behavior of the writing capacity C(G) for sequences of dense bidirectional graphs; this is given by C(G) = Ω(n/ ln n), where n is the number of nodes. A probabilistic method, Lovász local lemma (LLL), plays an essential role in deriving the asymptotic expression.

Original languageEnglish
Title of host publicationProceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1307-1311
Number of pages5
ISBN (Electronic)9781467377041
DOIs
Publication statusPublished - Sep 28 2015
EventIEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong
Duration: Jun 14 2015Jun 19 2015

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2015-June
ISSN (Print)2157-8095

Other

OtherIEEE International Symposium on Information Theory, ISIT 2015
CountryHong Kong
CityHong Kong
Period6/14/156/19/15

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

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  • Cite this

    Wadayama, T., Izumi, T., & Ono, H. (2015). Subgraph domatic problem and writing capacity of memory devices with restricted state transitions. In Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 (pp. 1307-1311). [7282667] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2015.7282667