Tom Whaley

Generating strings for bipartite Steinhaus graphs

Abstract Let b ( n ) be the number of bipartite Steinhaus graphs with n vertices. We show that b ( n ) satisfies the recurrence, b (2) = 2, b (3) = 4, and for k ⩾ 2, b (2 k + 1) = 2 b ( k + 1) + 1, b (2 k ) = b ( k ) + b ( k + 1). Thus b(n) ⩽ 5 2 n − 7 2 with equality when n is one more than a power of two. To prove this recurrence, we describe the possible generating strings for these bipartite graphs.

Characterizations of bipartite Steinhaus graphs

We characterize bipartite Steinhaus graphs in three ways by partitioning them into four classes and we describe the color sets for each of these classes. An interesting recursion had previously been given for the number of bipartite Steinhaus graphs and we give two fascinating closed forms for this recursion. Also, we exhibit a lower bound, which is achieved infinitely often, for the number of bipartite Steinhaus graphs.

Disconnected Complements of Steinhaus graphs

Abstract In 1976 Molluzzo asked for the conditions on a generating string of a Steinhaus graph that would guarantee that its complement would be connected. In this paper we give conditions that guarantee that the complement is not connected and a recursion, for the number of such strings. We also find tight upper and lower bounds for this recursion by examining the recursion d σ (2 k ) = d σ ( k )+ d σ ( k −1) and d σ (2 k +1) = 2 d σ ( k ) + 1.

The Alsos Digital Library for Nuclear Issues

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Parallel searches for hereditary node properties in binary trees

This paper is a progress report on our study of parallel algorithms to search a binary tree for nodes possessing a hereditary property. This problem was abstracted from a specific problem of this type having to do with the chromatic number of Steinhaus graphs. The algorithms discussed have been implemented and tested on this application using MPI. The assumption is that the time to test a node is significant; so the problem is to dynamically distribute nodes to the processors in such a way as to reasonably balance the work load.

Describing the CS forest to undergraduates (abstract)

While CS educators may agree that computer science involves much more than programming, different perspectives emerge concerning the introduction of non-programming topics within the first or second year of the undergraduate curriculum. Some common questions include: ● How can we give. beginning students a sense of the breadth of our discipline? ● What (non-programming) topics might be covered early in the curriculum? ● The Denning Report identifies major research areas within CS. How does this set of research topics relate to the topics which should be covered for undergraduates? ● Once we have identified appropriate topics to teach, how can we bring these ideas into the first few courses?

Alternative developments of cyclic-permutation algorithms

Abstract Feijen, van Gasteren, and Gries (1987) give a formal development of an algorithm to invert a cyclic permutation stored in an array, and Xue and Gries (1988) give such a development for an algorithm to cube a cyclic permutation. These derivations are first done with an alternative representation of the permutation; then a coordinate transformation is used to express the algorithm in terms of the array representation. Here, we develop the algorithms in terms of the original array, using the standard strategies.