Algorithms and properties of a new two-level network with folded hypercubes as basic modules

Abstract

In this paper, a new two-level interconnection network, called a hierarchical folded-hypercube network (HFN, for short), is proposed. The HFN takes folded hypercubes as basic modules which are connected in a complete manner. We investigate the topological properties of the HFN, including the diameter, cost, average distance, embedding, connectivity, container, rc-wide diameter, and node-fault diameter. We show that the HFN can emulate algorithms which are executable on the ring or the mesh-connected computer with the same time complexities in big-0 notation. Moreover, the HFN can embed a folded hypercube having the same number of nodes with constant dilation. We compute the diameter, node connectivity, best container, K-wide diameter, and node-fault diameter of the HFN. We present optimal routing and broadcasting algorithms for the HFN. The semigroup computation and descendascend algorithms can be executed as well on the HFN.

Fault‐tolerant cycle embedding in hierarchical cubic networks

“…Since the HCN(n) is regular of degree n ϩ 1, the result is optimal. The same result can be obtained for the hierarchical folded-hypercube network [6], which is a modification of the HCN. Throughout this section, we assume that the HCN(n) contains n Ϫ 1 link faults.…”

“…We also construct fault-free cycles of lengths at least 2 2n Ϫ 2f in an HCN(n) with f node faults, where 2 2n is the number of nodes in the HCN(n), f Յ n Ϫ 1 if n ϭ 3 or 4 and f Յ n if n Ն 5. Our results can be applied to the hierarchical folded-hypercube network [6] as well.…”

On the Rabin number problem

“…It is known from [13] (HFN(n, n)) if the Hamming distance between It has been shown in [13] that two nodes whose Hamming distance is n/2 / 1 have their (n / 1)-wide distance u n u n01 rrru 2 u 1 and s n s n01 rrrs 2 s 1 is n/2 and the Hamming distance between £ n £ n01 rrr£ 2 £ 1 and t n t n01 rrrt 2 t 1 is equal to D n/1 (FH(n)). For example, let us consider x (HFN(4, 4)) are con-0 1) [14].…”

Embedding Algorithms of Hierarchical Folded HyperStar Network

“…이러한 하이퍼큐브 연결망을 기반으로 하면 서 변형된 연결망 구조로 [1,7,12]이 있으며, 하이퍼큐브를 기반으로 계층적 상호연결망 형태를 갖는 HCN(n,n) [14], HFN(n,n) [3] 등이 분석되었다 [8,9,15]. 폴디드 하이퍼스타 연결망은 그 래프이론 관점에서 좋은 성질을 갖는 하이퍼스타 연결망의 지름(diameter)을 1/2 정도 개선하기 위해 제안된 연결망이 다 [9,16].…”