Hiroyuki Kawai

Factorization of de Bruijn digraphs by cycle-rooted trees

In this paper, we introduce a new concept of an arc-coloring of digraphs called in-coloring. An in-coloring of an in-regular digraph induces a factorization into cycle-rooted trees; a cycle-rooted tree is a weakly connected digraph in which every vertex has indegree one. In particular, we study in-colorings of a line digraph. The results interpolate one-factorizations and tree factorizations of the de Bruijn digraph.

A 40-nm resilient cache memory for dynamic variation tolerance with bit-enhancing memory and on-chip diagnosis structures delivering ×91 failure rate improvement

This paper presents a resilient cache memory for dynamic variation tolerance in a 40-nm CMOS. The cache can perform sustained operations under a large-amplitude voltage droop. To realize sustained operation, the resilient cache exploit 7T/14T bit-enhancing SRAM and on-chip voltage/temperature monitoring circuit. 7T/14T bit-enhancing SRAM can reconfigure itself dynamically to a reliable bit-enhancing mode. An on-chip monitoring circuit can sense a precise supply voltage level of a power rail of the cache. The proposed cache can dynamically change its operation mode using the voltage/temperature monitoring result and can operate reliably under a large-amplitude voltage droop. Experimental result shows that it does not fail with 25% and 30% droop of Vdd and it provides 91 times better failure rate with a 35% droop of Vdd compared with the conventional design. The processor simulator shows that the proposed cache running in the bit-enhancing mode results in 2.88% IPC loss on average.

Broadcasting Multiple Messages Using Cycle-Rooted Trees

In information dissemination problem on interconnection networks, problems of broadcasting and gossiping have been widely studied. In this paper, we study the other problem, called multi-source broadcasting, defined as follows: there are some (but not all) vertices each of which has the unique item of information and needs to disseminate to every other vertex. This problem is located at an intermediate position between broadcasting and gossiping. We analyze the multi-source broadcasting problem on the cycle-rooted tree and the de Bruijn digraph as an interconnection network.

Isomorphic factorization, the Kronecker product and the line digraph

In this paper, we investigate isomorphic factorizations of the Kronecker product graphs. Using these relations, it is shown that (1) the Kronecker product of the d-out-regular digraph and the complete symmetric digraph is factorized into the line digraph, (2) the Kronecker product of the Kautz digraph and the de Bruijn digraph is factorized into the Kautz digraph, (3) the Kronecker product of binary generalized de Bruijn digraphs is factorized into the binary generalized de Bruijn digraph.

Partitions, Functions and the Arc-Coloring of Digraphs

Let f and g be two maps from a set E into a set F such that f(x) ≠ g(x) for every x in E. Sahili [8] has shown that, if min{|f-1(z)|, |g-1(z)|} ≤ n for each z ∈ F, then E can be partitioned into at most 2n + 1 sets E1,..., E2n+1 such that f(Ei) g(Ei) = o for each i = 1,..., 2n + 1. He also asked if 2n + 1 is the best possible bound. By using Sahilis formulation of the problem in terms of the chromatic number of line digraphs, we improve the upper bound from 2n + 1 to O(log n). We also investigate extended version for more than two maps.