
Given the number of vertices
We discuss a parallel programming method for solving the maximum clique problem. We use the partitioned shared memory programming language, Unified Parallel C, for the parallel implementation. The problem of load balancing is discussed and the steal stack is used to solve this problem. Implementation details are provided.
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Splitting balanced incomplete block designs were first formulated by Ogata, Kurosawa, Stinson, and Saido recently in the investigation of authentication codes. This article investigates the existence of splitting balanced incomplete block designs, i.e.,
In this paper, we first present new proofs, much shorter and much simpler than can be found elsewhere, of two facts about Hypercubes: that for the
The search for special substructures in combinatorial objects that have a lot of symmetry, such as searching for maximal partial ovoids or spreads in generalized quadrangles, can often be translated to a well-known algorithmic problem, such as a maximum clique problem in a graph. These problems are typically NP-hard. However, using standard backtracking strategies together with pruning techniques based on problem-specific properties, it is possible to obtain non-trivial results which are mathematically interesting. In some cases, heuristic techniques can also lead to interesting results. In this paper, we describe some techniques as well as new results obtained for maximal partial ovoids and spreads in generalized quadrangles.
Built on earlier works of Larcombe on a certain class of non-terminating expansions of the sine function, we set up two new
In this paper, we investigate exhaustively the cyclically indecomposable triple systems
We show that if the independence number of a graph is
Let
In this paper, we establish a doubling method to construct inequivalent Hadamard matrices of order
In this paper, we determine analytically the number of balanced, unlabelled, 3-member covers of an unlabelled finite set, which is then used to find the number of non-isomorphic optimal lottery sets of cardinality three. We also determine numerically the number of non-isomorphic optimal playing sets for lotteries in which a single correct number is required to win a prize.
A fire breaks out on a graph
A construction is given for a Restricted Sarvate-Beam Triple System in the case
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We use a dynamic programming algorithm to establish a lower bound on the domination number of complete grid graphs
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