Abstract. An improved and general approach to connected-component labeling of images is presented. The algorithm presented in this paper processes images in predeterttuned order, which means that the processing order depends only on the image representation scheme and not on specific properties of the image. The algorithm handles a wide variety of image representation schemes (rasters, run lengths, quadtrees, bintrees, etc.). How to adapt the standard UNION-FIND algorithm to permit reuse of tempora~labels is shown. This is done using a technique called age balancing, in which, when two labels are merged, the older label becomes the father of the younger label. This technique can be made to coexist with the more conventional rule of wetghf balancing, in which the label with more descendants becomes the father of the label with fewer descendants. Various image scanning orders are examined and classified. It is also shown that when the algorithm is specialized to a pixel array scanned in raster order, the total processing time is linear in the number of pixels. The linear-time processing time follows from a special property of the UNION-FINDalgorithm, which maybe of independent interest. This property states that under certain restrictions on the input, UNION-FINDruns in time linear in the number of FIND and UNIONoperations. Under these restrictions, linear-time performance can be achieved without resorting to the more complicated Gabow-Tarj an algorithm for disjoint set union.
Large-scale distributed simulations model the activities of thousands of entities interacting in a virtual environment simulated over wide-area networks. Originally these systems used protocols that dictated that all entities broadcast messages about all activities, including remaining immobile or inactive, to all other entities, resulting in an explosion of incoming messages for all entities, most of which were of no interest. Using a filtering mechanism called interest management, some of these systems now allow entities to express interest in only the subset of information that is relevant to them. This paper surveys ten such systems, describing the purpose of the system, its scope, and the salient characteristics of its interest management scheme. We present the first taxonomy for such systems and classify the ten systems according to the taxonomy. The analysis of the classification reveals the fundamental nature of interest management and points to potential areas of research.
We present new graph-theoretical conditions for inscribable polyhedra and Delaunay triangulations. We establish several sufficient conditions of the following general form: if a polyhedron has a sufficiently rich collection of Hamiltonian subgraphs, then it is inscribable. These results have several consequences: • All 4-connected polyhedra are inscribable. • All simplicial polyhedra in which aU vertex degrees are between 4 and 6, inclusive, are inscribable. • AU triangulations without chords or nonfacial triangles are realizable as Delaunay triangulations. 'The support of the Committee on Research of the University of California, Irvine is gratefully acknowledged. 'By Lemma 2.2 of this paper, the result in [7] implies that any pyramid with a triangulated base is inscribable.
AbatractWe show that nondegenerate Delaunay triangulations satisfy a combinatorial property called ltoughness. A graph with set of sites S is l-tough if for any set P E S, c(S -P) 5 IS], where c(S -P) is the number of components of the subgraph induced by the complement of P and ]P] is the number of sites in P. We also show that, under the same conditions, the number of interior, components of S -P ia at most IPI -2. These appear to be the first nontrivial properties of a purely combinatorial nature to be established for Delaunay triangulations.We give examples to show that these bounds can be attained, and we state and prove several corollaries. In particular, we show that maximal planar graphs inscribable in a sphere are l-tough.
Abstract. We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straight-line edges and assign each edge to a layer so that no two edges on the same layer cross. The geometric thickness lies between two previously studied quantities, the (graph-theoretical) thickness and the book thickness. We investigate the geometric thickness of the family of complete graphs, {Kn}. We show that the geometric thickness of Kn lies between (n/5.646) + 0.342 and n/4 , and we give exact values of the geometric thickness of Kn for n ≤ 12 and n ∈ {15, 16}.
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