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A Fast Distributed Routing Algorithm for Supertoroidal Networks
Abstract: "Supertoroidal networks are based upon Cayley graphs of semi-direct products of cyclic groups. This paper approaches the semi- direct product of groups and an associated Cayley graph from a perspective which emphasizes its product structure in order to illiminate similarites with more familiar graphs which are based upon products of cycles. This approach leads in a very natural way to a class of suboptimal routing algorithms on supertoroidal networks. These algorithms can be distributed to the nodes of the network and can be implemented in logic rather than look-up tables. The paper includes an analysis of the algorithmic diameter of the network."
Synchronous Algorithms on [gamma](4,1,1)
The work reported on in this paper is directly related to other work conducted at SRC. The embeddings obtained for the sixty-four node graph can be implemented on the network testbed, H-Net, being developed at SRC. These embeddings are also of interest because Duncan Buell recently found embeddings of butterflies in supertoroidal networks by an enlightened computer search. A comparison of the results in this paper and the results found by Buell are included."
Bulletin
None
The Diameter and Mean Diameter of Supertoroidal Networks
Abstract: "Supertoroidal networks are Cayley graphs of noncommutative groups. They are of degree four and are closely related to the k-ary 3-cubes of comparable size. Supertoroidal networks have smaller diameter and average diameter than k-ary 3-cubes, thereby providing a design alternative which reduces the pin complexity of wide data path interprocessor communication in tightly coupled multiprocessor systems. In this paper, we calculate the diameter and an asymptotic bound for the mean diameter of supertoroidal networks."
A Parallel Approach to CRC Encoding
Abstract: "The emergence of high-speed gigabit networks such as ATM has prompted a need for fast error-control mechanisms. CRCs have the distinction of being one of the most popular and simple fault tolerant implementations in use today. Traditionally, they are computed serially in lockstep with outgoing or incoming datagrams; this approach can become difficult, if not impossible, when applied to high-speed networking. Our study of CRCs has yielded a parallel algorithm that can compute a CRC for any arbitrary length datagram. For example, 937 XORs are required to calculate an IEEE-802 CRC-32 for a 64-bit word; large datagrams can be broken down into a group of 64-bit cells and have their CRCs constructed as each cell is transmitted across a network. Clearly, this serial and parallel approach is more efficient than the traditional lockstep scheme. Using a fast FPGA, a CRC-32 for a 64-bit cell can be calculated in three or four levels of combinatorial logic. A custom-made ASIC could potentially calculate a CRC in as fast as 10 ns."
Publications of the Colonial Society of Massachusetts
Primarily consists of: Transactions, v. 1, 3, 5-8, 10-14, 17-21, 24-28, 32, 34-35, 38, 42-43; and: Collections, v. 2, 4, 9, 15-16, 22-23, 29-31, 33, 36-37, 39-41; also includes lists of members.
The War of the Rebellion: v. 1-53 [serial no. 1-111] Formal reports, both Union and Confederate, of the first seizures of United States property in the southern states, and of all military operations in the field, with the correspondence, order and returns relating specially thereto. 1880-1898. 111 v
Official records produced by the armies of the United States and the Confederacy, and the executive branches of their respective governments, concerning the military operations of the Civil War, and prisoners of war or prisoners of state. Also annual reports of military departments, calls for troops, correspondence between national and state governments, correspondence between Union and Confederate officials. The final volume includes a synopsis, general index, special index for various military divisions, and background information on how these documents were collected and published. Accompanied by an atlas.
Supertoroidal Networks
Abstract: "The objective of this paper is to define supertoroidal networks, to describe several physical layouts and to expose their scalability. These networks are Cayley graphs of noncommutative groups. They are of degree four and are closely related to the k-ary 3-cubes of comparable size. Supertoroidal networks have smaller diameter and average diameter than k-ary 3-cubes, thereby providing a design alternative which reduces the pin complexity of wide data path interprocessor communication in tightly coupled multiprocessor systems."
