Properties and Algorithms of the KCube Interconnection Networks

The KCube interconnection network was first introduced in 2010 in order to exploit the good characteristics of two well-known interconnection networks, the hypercube and the Kautz graph. KCube links up multiple processors in a communication network with high density for a fixed degree. Since the KCube network is newly proposed, much study is required to demonstrate its potential properties and algorithms that can be designed to solve parallel computation problems. In this thesis we introduce a new methodology to construct the KCube graph. Also, with regard to this new approach, we will prove its Hamiltonicity in the general KC(m; k). Moreover, we will find its connectivity followed by an optimal broadcasting scheme in which a source node containing a message is to communicate it with all other processors. In addition to KCube networks, we have studied a version of the routing problem in the traditional hypercube, investigating this problem: whether there exists a shortest path in a Qn between two nodes 0n and 1n, when the network is experiencing failed components. We first conditionally discuss this problem when there is a constraint on the number of faulty nodes, and subsequently introduce an algorithm to tackle the problem without restrictions on the number of nodes.

Bundling under the Threat of Parallel Trade

This paper examines the use of bundling by a firm that sells in two national markets and faces entry by parallel traders. The firm can bundle its main product, - a tradable good- with a non-traded service. It chooses between the strategies of pure bundling, mixed bundling and no bundling. The paper shows that in the low-price country the threat of grey trade elicits a move from mixed bundling, or no bundling, towards pure bundling. It encourages a move from pure bundling towards mixes bundling or no bundling in the high-price country. The set of parameter values for which the profit maximizing strategy is not to supply the low price country is smaller than in the absence of bundling. The welfare effects of deterrence of grey trade are not those found in conventional models of price arbitrage. Some consumers in the low-price country may gain from the threat of entry by parallel traders although they pay a higher price. This is due to the fact that the firm responds to the threat of arbitrageurs by increasing the amount of services it puts in the bundle targeted at consumers in that country. Similarly, the threat of parallel trade may affect some consumers in the hight-price country adversely.