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Given an undirected distance graph G=(V, E, d) and a set S, where V is the set of vertices in G, E is the set of edges in G, d is a distance function which maps E into the set of nonnegative numbers and S⊑V is a subset of the vertices of V, the Steiner tree problem is to find a tree of G that spans S with minimal total distance on its edges. In this paper,(More)
Given a set, S, of Boolean n-vectors, one can choose k of the n coordinate positions and consider the set of k-vectors which results by keeping only the designated k positions of each vector, i.e., from k-projecting S. In this paper, we study the question of finding sets S as small as possible such that every k-projection of S yields all the 2 k possible(More)
Given a sequence of positive weights, W=w 1≧...≧w n >0, there is a Huffman tree, T↑ (“T-up”) which minimizes the following functions: max{d(wi)}; Σd(wi); Σf(d(wi)) w i(here d(w i) represents the distance of a leaf of weight w i to the root and f is a function defined for nonnegative integers having the property that g(x) = f(x + 1) − f(x) is monotone(More)
A set composed of 27 phages is described for differentiating Salmonella spp. representative of groups A, B, C1, C2, D1, D2, E1, E2, E3, E4, G1, K, and N. All of the 1,245 cultures used in this effort were typable and were differentiated on the basis of the 420 phage patterns observed. All results were reproducible. Characteristic phage patterns were(More)
In this paper we consider the question of how much space is needed to represent a set. Given a finite universe U and some subset V (called the vocabulary), an <underline>exact membership tester</underline> is a procedure that for each element s in U determines if s is in V. An <underline>approximate membership tester</underline> is allowed to make mistakes:(More)
Given partially ordered sets (posets) P and Q, it is often useful to construct maps g:P&#x02192;Q which are chain-continuous: least upper bounds (supremums) of nonempty linearly ordered subsets are preserved. Chaincontinuity is analogous to topological continuity and is generally much more difficult to verify than isotonicity: the preservation of the order(More)