TY - GEN

T1 - Subgraph domatic problem and writing capacity of memory devices with restricted state transitions

AU - Wadayama, Tadashi

AU - Izumi, Taisuke

AU - Ono, Hirotaka

N1 - Funding Information:
This work is supported by a JSPS Grant-in-Aid for Scientific Research (B) Grant Number 25289114.
Publisher Copyright:
© 2015 IEEE.

PY - 2015/9/28

Y1 - 2015/9/28

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84969760084&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84969760084&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2015.7282667

DO - 10.1109/ISIT.2015.7282667

M3 - Conference contribution

AN - SCOPUS:84969760084

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1307

EP - 1311

BT - Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - IEEE International Symposium on Information Theory, ISIT 2015

Y2 - 14 June 2015 through 19 June 2015

ER -