
Let
Regular graphs play an important role in designing interconnection networks for multiprocessing systems; but these regular graphs like hypercubes or star graphs cannot be constructed with an arbitrary number of nodes. The purpose of the present paper is to examine two families of almost regular maximally fault tolerant graphs (based on hypercubes and star graphs respectively) that can be defined for an arbitrary number of nodes.
We consider the problem of minimizing total flow time for the imprecise computation model introduced by Lin et al. Leung et al. have shown that the problem of finding a minimum total flow time schedule subject to the constraint that the total error is no more than a given threshold
A
To determine the error-correcting capability of a large error-correcting code it may be necessary to generate the code, an intractable task. Using a stack-based algorithm and utilizing structural properties of a code can reduce the time required. Timing results are reported for generating large codes using these methods on massively parallel platforms.
Consider a queue of
A simple new proof of an existence condition for periodic complementary binary sequences is given. In addition, this result is extended to the general case, which was previously unsolved.
Token-passing algorithms are a well-known way of solving distributed mutual exclusion problems in computer networks. A simple abstraction of the concept of tokens allows the use of elementary constructions in general hypergraphs to show that certain sets of tokens are minimal. This suggests other problems about hypergraphs worthy of exploration. As an application, we introduce a new mutual exclusion problem, the
A PBD construction for six MOLS of order
Two algorithms to compute monotone stabbers for convex polygons are presented. More precisely, given a set of
Several algorithms for geometric constructions on the real projective plane are described. These methods also apply to Euclidean plane geometry. The concept of an augmented determining set is fundamental to the algorithms. A backtracking algorithm to find augmented determining sets is described. Algorithms for animating constructions, and an incidence-forcing algorithm are also presented. These algorithms have been implemented on an
A tournament design,
We provide two new upper bounds on the total chromatic number of all hypergraphs and give two conjectures related to both the Total Colouring Conjecture for graphs and the Erdős-Faber-Lovász Conjecture.
The first serious mathematical study of whist tournament designs was carried out in the 1890s by E.H. Moore. In this survey, I shall outline briefly the subsequent work which culminated in the proof of the existence of whist tournaments of all possible orders by Baker, Wilson, and Hanani in the 1970s, and then describe some more recent work, mainly by N.J. Finizio, Y.S. Liaw, and the author, on the construction of cyclic whist tournaments. In particular, triple whist tournaments will be discussed.
A graph
The problem of finding the distance between two graphs is known to be NP-complete. In this paper, we describe a heuristic algorithm that uses simulated annealing to find an upper bound for the distance between two graphs. One of the motivations for developing such an algorithm comes from our interest in finding the diameter of families of non-isomorphic extremal graphs. We tested our algorithm on each family of extremal graphs with up to
Here we present
There are many graphs with the property that every subgraph of a given simple isomorphism type can be completed to a larger subgraph which is embedded in its ambient parent graph in a nice way. Often, such graphs can be classified up to isomorphism. Here we survey theorems on polar space graphs, graphs with the cotriangle property, copolar graphs, Fischer spaces, and generalized Fischer spaces, as well as graphs with the odd coclique property.
Permutation graphs, a well-known class of perfect graphs, has attracted the attention of numerous researchers. There are two noteworthy representations of permutation graphs. Permutation diagrams have been widely employed in theoretical and application research. The
In this paper, we investigate the relationship between the profiles of Hadamard matrices and the weights of the doubly even self-orthogonal/dual
Let
The Balanced Network Search (BNS) is an algorithm which finds a maximum balanced flow in a balanced network
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