In a seminal STOC’95 paper, Arya et al. [4] devised a construction that for any set S of n points in R and any ǫ > 0, provides a (1 + ǫ)-spanner with diameter O(log n), weight O(log n)w(MST (S)), and constant maximum degree. Another construction of [4] provides a (1 + ǫ)-spanner with O(n) edges and diameter α(n), where α stands for the inverse-Ackermann function. Das and Narasimhan [18] devised...

A minimum spanning tree (MST) with a small diameter is required in numerous practical situations. It is needed, for example, in distributed mutual exclusion algorithms in order to minimize the number of messages communicated among processors per critical section. Understanding the behavior of tree diameter is useful, for example, in determining an upper bound on the expected number of links bet...

Let G be an edge weighted undirected graph. For every pair of nodes consider the shortest cycle containing these nodes in G. The cycle diameter of G is the maximum length of a cycle in this set. Let H be a directed graph obtained by directing the edges of G. The cycle diameter of H is similarly defined except for that cycles are replaced by directed closed walks. Is there always an orientation ...

In this paper we introduce a new interconnection network Fault Tolerant Hierarchical Interconnection network for parallel Computers denoted by FTH(k, 1).This network has fault tolerant hierarchical structure which overcomes the fault tolerant properties of Extended hypercube(EH).This network has low diameter, constant degree connectivity and low message traffic density in comparisons with other...

Shuffle-exchange networks have been proposed as an attractive choice for interconnection networks. They have constant node degree and sublogarithmic diameter. Several researchers have studied various combinatorial and interconnection properties of them. In this paper, we generalize shuffle-exchange networks and define a new class of networks, called generalized shuffle-exchange network and deno...

A new interconnection network for massively parallel computing is introduced. This network is called an Optical Multi-Mesh Hypercube (OMMH) network. The OMMH integrates positive features of both hypercube (small diameter, high connectivity, symmetry, simple control and routing, fault tolerance, etc.) and mesh (constant node degree and scalability) topologies and at the same time circumvents the...

We were intrigued by the article by Mount et al1 on the reversal of hemophilia B following the intraportal injection of an adenoassociated viral vector encoded with the coagulation factor IX gene into hemophiliac dogs. Mount et al reported substantial correction of hemophilia B in 3 of the 4 animals. However, we think that the fourth dog, Beech, is more interesting. He obtained only temporary r...

Our purpose was to evaluate hyporesponsivity to nitric oxide (NO)-induced dilation in small arterioles during nitrate tolerance. An Alza osmotic pump was implanted in the left flank of adult rats (n = 56) for continuous administration of nitroglycerin (140 microg/h) or vehicle (propylene glycol). On postoperative day 3, arcade (approximately 50-microm diameter) and terminal (approximately 20 mi...