Let S be a metric space under the distance function d. A metric baris is a subset B c S such that d(b, x) = d(b, y) for all b E B implies x = y. It is shown that for Euclidean distance, the minimalâ€¦ (More)

Given two sets of M points on a line or on a circle, a minimal matching between them is found in 0( M log M) time. The circular case, where the distance between two points is the length of â€˜theâ€¦ (More)

The boolear? distance between twc points x and y of a connected graph G is defined as the set of all points on all paths joining x and y in G (@ if x = y). It is determined in terms of theâ€¦ (More)

Consider the following two graphs M a n d N, both with vertex set ZÃ—Z, where Z is the set of all integers. In M, two vertices are adjacent when their euclidean distance is 1, while in N, adjacency isâ€¦ (More)

An additional convexity condition is given to correct a theorem characterizing city block distance. Key words': City block distance. The author is grateful to Dr. Christian Ronse of Philips Researchâ€¦ (More)

A graph can be metrized by assigning a length to each of its edges. Such a graph is said to be geodetic if for each pair of vertices there is a unique geodesic joining them. It is said to be normallyâ€¦ (More)

We consider the graphs of functions representable in the form h(x) = ~= t aJj(x) where the f) constitute a linearly independent set of functions over R. These graphs are digitized by the set ofâ€¦ (More)