The St. Catharines Star, Vol.1 Iss. 1

Tuesday, January 5th, 1971

Properties and algorithms of the (n, k)-star graphs

The (n, k)-star interconnection network was proposed in 1995 as an attractive alternative to the n-star topology in parallel computation. The (n, k )-star has significant advantages over the n-star which itself was proposed as an attractive alternative to the popular hypercube. The major advantage of the (n, k )-star network is its scalability, which makes it more flexible than the n-star as an interconnection network. In this thesis, we will focus on finding graph theoretical properties of the (n, k )-star as well as developing parallel algorithms that run on this network. The basic topological properties of the (n, k )-star are first studied. These are useful since they can be used to develop efficient algorithms on this network. We then study the (n, k )-star network from algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms for basic communication, prefix computation, and sorting, etc. A literature review of the state-of-the-art in relation to the (n, k )-star network as well as some open problems in this area are also provided.

Properties and algorithms of the hyper-star graph and its related graphs

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also been designed. This thesis studies the hyper-star graph from both the topological and algorithmic point of view. For the topological properties, we try to establish relationships between hyper-star graphs with other known graphs. We also give a formal equation for the surface area of the graph. Another topological property we are interested in is the Hamiltonicity problem of this graph. For the algorithms, we design an all-port broadcasting algorithm and a single-port neighbourhood broadcasting algorithm for the regular form of the hyper-star graphs. These algorithms are both optimal time-wise. Furthermore, we prove that the folded hyper-star, a variation of the hyper-star, to be maixmally fault-tolerant.

Advertisement Star Music Store

An advertisement for Star Music Store, established 1869. The advertisement describes the services offered and the brands sold.

Receipt from W.H. Eckhardt, Star Music Store, St. Catharines for rent of machine

Receipt from W.H. Eckhardt, Star Music Store, St. Catharines for rent of machine, Feb. 1, 1888.

Letter to H.H. Collier of the Auditor’s Office in Austin, Texas from D.W. Fitch, publisher of the Houston Star Newspaper

Letter to H.H. Collier of the Auditor’s Office in Austin, Texas from D.W. Fitch (3 pages, handwritten), publisher of the Houston Star Newspaper. The letter is about newspaper business and personal matters. It is stated that Henry might go to Austin. This letter has been torn and taped. This does not affect the text, Feb. 28, 1841.

The Evening Star, August 16, 1900

The Evening Star, St. Catharines, Ontario. This paper contains an advertisement for James D. Tait Company, August 16, 1900.

The Evening Star, January 7, 1902

The Evening Star, St. Catharines, Ontario. This paper contains an advertisement for James D. Tait Company, January 7, 1902.