Cycles in folded hypercubes

Multilayer VLSI Layout for Interconnection Networks

Current VLSI technology allows more than two wiring layers and the number is expected to rise in future. In this paper, we show that, by designing VLSI layouts directly for an L-layer model, the layout area for a variety of networks can be reduced by a factor of about L 2 2 compared to the layout area required under a 2-layer model, and the volume and maximum wire length can be reduced by a fac...

Efficient VLSI Layouts of Hypercubic Networks

In this paper, we present efficient VLSI layouts of several hypercubic networks. We show that an N-node hypercube and an N-node cube-connected cycles (CCC) graph can be laid out in 4N2=9 + o(N2) and 4N2=(9log22 N) + o(N2= log2 N) areas, respectively, both of which are optimal within a factor of 1:7̄+ o(1). We introduce the multilayer grid model, and present efficient layouts of hypercubes that u...

1-vertex-fault-tolerant Cycles Embedding on Folded Hypercubes

In this paper, we focus on a hypercube-like structure, the folded hypercube, which is basically a standard hypercube with some extra links between its nodes. Let f be a faulty vertex in an n-dimensional folded hypercube FQn. We show that FQn−{f } contains a faultfree cycle of every even length from 4 to 2n−2 if n ≥ 3 and, furthermore, every odd length from n+ 1 to 2n − 1 if n ≥ 2 and n is even....

Fault-Free Cycles in Conditional Faulty Folded Hypercubes

An n-dimensional folded hypercube FQn is an attractive variance of an n-dimensional hypercube Qn, which is obtained by a standard hypercube with some extra edges established between its vertices. FQn for any odd n is known to be bipartite. In this paper, for any FQn (n ≥ 2) with at most 2n−3 faulty edges in which each vertex is incident with at least two fault-free edges, we prove that there ex...

Edge-fault-tolerant properties of hypercubes and folded hypercubes