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arXiv · 1501.04402

Subgraph Domatic Problem and Writing Capacity of Memory Devises with Restricted State Transitions

Tadashi Wadayama·Taizuke Izumi·Hirotaka Ono
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Abstract

A code design problem for memory devises 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 a valid coloring with the largest number of colors for a subgraph of a given directed graph. The number of colors in an optimal valid coloring gives the writing capacity of a given 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, that is given by C(G)=Omega(n/ln n) where n is the number of nodes. A probabilistic method called Lovasz local lemma (LLL) plays an essential role to derive the asymptotic expression.

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Tadashi Wadayama, Taizuke Izumi, Hirotaka Ono. 2015-01-19. Subgraph Domatic Problem and Writing Capacity of Memory Devises with Restricted State Transitions. https://arxiv.org/abs/1501.04402

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