J. W. Jaromczyk and Godfried T. Toussaint. Relative neighborhood graphs and their relatives. Proceedings of the IEEE, 80(9):1502-1517, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....So we can easily see that # skeletons contain Gabriel graph and Relative neighborhood graph. Specially, when #=1, G 1 (V ) GG(V ) Gabriel graph of V ; when #=2, G 2 (V ) RNG(V ) Relative neighborhood graph of V . According to the feature of # skeleton, it is easy to see that RNG(V ) # GG(V ) [9]. If we change slightly the definition of the neighborhood by using the different intersection of the spheres, we can obtain a different class of graphs. In the following section, we will design a uniform algorithm for the whole spectrum of # skeletons for 1 # # # 2. 3. EXPERIMENTS AND RESULTS ....

J.W. Jaromczyk and G.T. Toussaint. Relative neighborhood graphs and their relatives. Proceedings IEEE, 80(9):1502--1517, 1992.

....that u and v are close enough to each other to be connected by an edge. Depending on the application context, different definitions of region of influence and of corresponding proximity graphs have been proposed in the literature. A comprehensive survey is given by Jaromczyk and Toussaint [10]; here we only recall some of the most widely studied proximity graphs. Two continuous hierarchies of proximity graphs that includes Gabriel graphs and relative neighbourhood graphs as special cases were first defined in the computational morphology context by Kirkpatrick and Radke [13] The ....

J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 80(9) 1502--1517, 1992.

....is the work described in [6, 12] although it does not deal directly with topology control, the notion of # graph used in these papers bears some resemblance to the cone based idea described in this paper. Relative neighborhood graphs [24] and their relatives (such as Gabriel graphs, or G # graphs [10]) are similar in spirit to the graphs produced by the cone based algorithm. The rest of the paper is organized as follows. Section 2 presents the basic cone based algorithm and shows that # = 5# 6 is necessary and su#cient for connectivity. Section 3 describes several optimizations to the basic ....

J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 80:1502--1517, 1992.

....interior of the intersection Bu; kuvk Bv; the lune, denoted by luneu; v, defined by two points u and v. The constrained relative neighborhood graph RNGV over a point set V has an edge and the luneu; v does not contain any point from V in the interior. Toussaint and Jaromczyk [11] [12] gave the first definition of the relative neighborhood graph to study the pattern recognition. The constrained Gabriel graph of a point set V , denoted by GGV consists of all edges uv such that and the disku; v does not contain any node from V . Gabriel and Sokal [13] defined the Gabriel ....

J.W. Jaromczyk and G.T. Toussaint, "Relative Neighborhood Graphs and Their Relatives," Proc. IEEE, vol. 80, no. 9, pp. 15021517, 1992.

.... not explored much until the early 1990s (although there was a lot of closely related work on coverage processes and poisson point processes, when work on disk graphs (see, e.g. CC90] GraSW94] interval graphs (see, e.g. GoH97] sphere of in uence graphs (see, e.g. DLL94] [JT92], To82] and random graphs on Euclidean space (see, e.g. St94] M99] started to appear. In this paper, we will explore a one dimensional version of this model of random graphs. Random graphs became a research topic as opposed to a research tool after the seminal paper of Erd os and ....

J. Jaromczyk & G. Toussaint, Relative neighborhood graphs and their relatives, Proc. IEEE 80 (1992), 1502-1517; CSA 0014664.

....neighbourhood graph approach [5] builds and searches an approximate local neighbourhood graph. Eppstein et al. 18] investigated the fundamental properties of a nearest neighbour graph. Jaromczyk and Toussaint surveyed data structures and techniques based on Relative Neighbourhood Graphs [34]. Graph based techniques tend to have the same di#culties as tree based approaches: searching a graph also involves stacks or queues, dependent memory accesses, and pointerchasing unsuited to high latency pipelined memory access. Point Location Voronoi diagrams can be used for optimal 1 nearest ....

J. W. Jaromczyk and G. T. Toussaint. Relative Neighborhood Graphs and Their Relatives. Proc. IEEE, 80(9):1502--1517, September 1992. 2.2

..... there is a whole variety of theoretical geo metric concepts, trying to capture vague and ill defined notions like proximity, structure, and shape, and all share a surprisingly large number of potential application areas in science and engineering. Refer to Jaromczyk and Toussaint [43] for a survey and bibliography on relative neigh borhood graphs and their variants, including a list of applications in computational morphology, computer vision, geographic analysis, and pattern recognition. Three dimensional alpha shapes are particularly close to real life applications. For ....

J W Jaromczyk and G T Toussaint. Relative neighborhood graphs and their relatives. Proceedings of the IEEE, 80(9):1502 1571, 1992.

.... analysis, geographic information systems, computational geometry, computational morphology, and computer vision use the underlying structure (also referred to as the skeleton or internal shape) of a set of data points revealed by means of a proximity graph (see for example [16] 13] 7] [9]) A proximity graph attempts to exhibit the relation between points in a point set. Two points are joined by an edge if they are deemed close by some proximity measure. It is the measure that determines the type of graph that results. Many di erent measures of proximity have been de ned, giving ....

....measure. It is the measure that determines the type of graph that results. Many di erent measures of proximity have been de ned, giving rise to many di erent types of proximity graphs. An extensive survey on the current research in proximity graphs can be found in Jaromczyk and Toussaint [9]. We are concerned with the spanning ratio of proximity graphs. Consider n points in IR , and de ne a graph on these points, such as the Gabriel graph [8] or the relative neighborhood graph [16] For a pair of data points (u; v) the length of the shortest path measured by Euclidean distance ....

J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proceedings of the IEEE, 80(9), pp. 1502-1517, 1992.

....measure, computing in this way a graph, called a proximity graph, associated to the set of points. Many di erent measures of proximity have been de ned (each giving rise to di erent types of proximity graphs) and among them the proximity regions described above play a central role [19] 22] 24] [14]. If, for example, one wishes to give a set of points the shape of a tree, it is necessary to determine which proximity regions will induce on the points such a shape. The results presented in this paper allow us to answer this type of question. Finally, proximity drawing problems may be viewed ....

J. W. Jaromczyk and G. T. Toussaint. Relative Neighborhood Graphs and Their Relatives. Proceedings of the IEEE, 80, 1992, pp. 1502-1517.

....McGill University. liotta infokit.ing.uniroma1.it Other proximity graphs that have been studied are the fi skeleton [12] the sphere of influence graph [25] and the fl neighborhood graph [27] An extensive survey on the current research in proximity graphs can be found in Jaromczyk and Toussaint [14]. Much attention has been given over the past several years to developing algorithms for drawing graphs in the plane such that the resulting drawing has certain geometric properties. For example, Dillencourt [6] showed that any triangulation without chords or nonfacial triangles is drawable as a ....

J. W. Jaromczyk and G. T. Toussaint. Relative Neighborhood Graphs and Their Relatives. Proceedings of the IEEE, 80, 9, 1992, pp. 1502-1517.

....on the size of such graphs. Toussaint [28] introduced the sphere of influence graph and proposed an O(n log n) algorithm for computing the sphere of influence graph of n points in the plane. An extensive survey on the current research in proximity graphs can be found in Jaromczyk and Toussaint [16]. In this paper we tackle the proximity graph drawability problem, i.e. the problem of characterizing graphs that can be drawn as certain types of proximity graphs. A graph G can be drawn as a proximity graph if there exists a set of points in the plane whose proximity graph is isomorphic to G. ....

J. W. Jaromczyk and G. T. Toussaint. Relative Neighborhood Graphs and Their Relatives. Proceedings of the IEEE, 80, 1992, pp. 1502-1517.

....measure. The measure determines the type of graph that results; many different measures of proximity have been defined and studied. Proximity graphs have been studied in the context of pattern recognition, geographic variation analysis, computational geometry, graph theory, and graph drawing. See [10] for a survey of this area. The combinatorial structure of interest in this paper is the tree, which is well studied in the literature. For example, the study of spanning trees of a set of points has a long history. From a graph drawing perspective (see [6] for a survey of graph drawing) the ....

J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 80(9):1502--1517, Sept. 1992.

....Wilson s algorithm [9] but using the graph neighbours of each sample instead of the Euclidean or other norm based distance neighbourhood. Two samples x and y are graph neighbours in a PG, G = V,E) if there exists an edge (x, y) # E between them. Taking into account the definitions of GG and RNG [15,16], the graph neighbourhood of a given point requires that no other point lies inside the union of the zones of influence (i.e. hypersphere or lune of influence) corresponding to all its graph neighbours. See Appendix I for a careful definition of GG and RNG, along with an algorithm to generate ....

Jaromczyk JW, Tourssaint GT. Relative neighborhood graphs and their relatives. Proceedings of the IEEE 1992; 80:1502--1517

....is the work described in [3, 7] although it does not deal directly with topology control, the notion of # graph used in these papers bears some resemblance to the conebased idea described in this paper. Relative neighborhood graphs [15] and their relatives (such as Gabriel graphs, or G# graphs [5]) are similar in spirit to the graphs produced by the cone based algorithm. The rest of the paper is organized as follows. Section 2 presents the basic cone based algorithm and shows that # = 5# 6 is necessary and su#cient for connectivity. Section 3 describes several optimizations to the basic ....

J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 80:1502--1517, 1992.

....values of fi such that fi 1 the fi skeleton is planar. fi skeletons have been receiving much attention during the years (see, e.g. 1, 5, 10, 16] A rich body of papers have been published which describe effective algorithms for computing proximity graphs. For a survey on the topic see also [4]. Roughly, they can be classified according to whether they assume the Fixed Proximity Scenario or whether they assume the Variable Proximity Scenario. Fixed Proximity Scenario: In the fixed proximity scenario it is known a priori what is the best definition of closeness to use for reconstructing ....

J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 80(9):1502--1517, September 1992.

....open problem to decide whether this problem can be solved in linear time if EMST (S) is given as part of the input. In the rest of this section we focus on another subgraph of DT (S) the all nearest neighbors graph, which has been used as a tool for collecting proximity information of the set S [14]. Let nn(p i ) denote the nearest neighbor of p i in the set S. The (directed) graph ANN (S) is defined as follows: p i is connected to p j if and only if p j = nn(p i ) When dealing with inexact data or moving points, the tolerance of this structure is again a useful tool. More generally, we ....

J. W. Jaromczyk and G. T. Toussaint, Relative Neighborhood Graphs and Their Relatives, Proc. IEEE 80 (1992) 1502-1517.

....geographic variation analysis, geographic information systems, computational geometry, computational morphology, and computer vision. For a complete survey on the different definitions of proximity and on application areas, the reader is referred to the survey paper by Jaromczyk and Toussaint [17]. A widely accepted way for capturing the notion of proximity between points is to use the concept of region of influence (also called proximity region) Given a pair u; v of points in the plane, the proximity region of u and v is a portion of the plane, determined by u and v, that contains ....

J. W. Jaromczyk and G. T. Toussaint. Relative Neighborhood Graphs and Their Relatives. Proceedings of the IEEE, 80, 1992, pp. 1502-1517.

....of two (open) disks whose radius is the distance from p to q, with one disk centered at p and the other at q; the corresponding graph is called the relative neighborhood graph [49] See the examples in Figure 12. For a survey on proximity graphs and on their applications to graph drawing see [24] and [16] The Proximity Server of GS can generate infinitely many proximity graphs on a given set S. The user, through the canvas of the hypertextual interface, specifies both the set S and a nonnegative parameter fi. This parameter unambiguously defines the shape of the proximity region, called ....

J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 80(9):1502--1517, Sept. 1992.

....that joins pairs of points so that the resulting graph is perceptually meaningful in some sense (for more details on these problems see also [25] Several graphs that capture the notion of shape of a set S of points on the plane have been described in the literature. In the survey by Toussaint [15] such graphs are classified by using the notion of proximity between sets of points. In a proximity graph points are connected by edges if and only if they are deemed close by some proximity measure. It is the measure that determines the type of graphs that result. Minimum spanning trees [22] ....

....diagram in O(nff(n; n) time, where ff( Delta) is the inverse of the Ackermann s function. The bound is reduced to O(n) by Jaromczyk, Kowaluk, and Yao [14] A different proof of this last result is given by Lingas [17] For a complete survey on algorithms that compute proximity drawings see [15]. Existing algorithms, however, often accomplish the asymptotically optimal efficiency at the expenses of simplicity; also they often rely on simplifying assumptions on the input configuration (no three points are collinear and no four points are co circular) that make them fail when implemented ....

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J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 80(9):1502-- 1517, Sept. 1992.

....geographic information systems, computational geometry, computational morphology, and computer vision. For a complete survey on the different types of proximity regions and their corresponding skeletons and on application areas, the reader is referred to the survey paper by Jaromczyk and Toussaint [17]. While techniques have been designed for the efficient computation of the skeleton of a given set of points, the problem of determining which graphs have proximity drawings has only just begun to be studied. The proximity drawability testing problem is to determine, for a given definition of ....

J. W. Jaromczyk and G. T. Toussaint. Relative Neighborhood Graphs and Their Relatives. Proceedings of the IEEE, 80, 1992, pp. 1502-1517.

....been developed to characterize both the external shape (convex hull, ff hull) and the internal shape (nearest neighbor graph, minimum spanning tree, relative neighborhood graph, Gabriel graph, and Delaunay triangulation) of a point set. For an overview of these descriptors we refer the reader to [11], 20] and references therein. Computing a skeletal description for such shapes is of particular interest not only because skeletons provide an intuitive shape description, but also because of the wide use of skeletons as shape descriptors and the possible applicability of such a technique in ....

J. W. Jaromczyk and G. T. Toussaint. "Relative Neighborhood Graphs and their Relatives". Proceedings of IEEE, 80(9):1502--1517, 1992.

....its total length, needs to be bounded by a factor f . In particular, every (strong) f spanner is a weak f spanner for some f at most as large as f , usually substantially smaller. Starting with Yao [28] spanners for given P are usually computed by a generalization of proximity graphs [17]: Partition IR D into k 2 IN convex cones C 0 ; C k Gamma1 . Then, from vertex p 2 P, draw directed edges (arcs) to the closest point of P lying in the translated cone p C j ; do this for j = 0 : k Gamma 1. The resulting graph is called a partitioned neighborhood graph (PNG) Its ....

J.W. Jaromczyk and G.T. Toussaint: "Relative Neighborhood Graphs and Their Relatives", Proceedings of IEEE 80, 1992, 1502-1517.

.... analysis, geographic information systems, computational geometry, computational morphology, and computer vision use the underlying structure (also referred to as the skeleton or internal shape) of a set of data points revealed by means of a proximity graph (see for example [16] 13] 7] [9]) A proximity graph attempts to exhibit the relation between points in a point set. Two points are joined by an edge if they are deemed close by some proximity measure. It is the measure that determines the type of graph that results. Many different measures of proximity have been defined, giving ....

....measure. It is the measure that determines the type of graph that results. Many different measures of proximity have been defined, giving rise to many different types of proximity graphs. An extensive survey on the current research in proximity graphs can be found in Jaromczyk and Toussaint [9]. Research supported by NSERC Grant OGP0183877 and a FIR Grant. D epartement de Math ematiques et d Informatique, Universit e du Qu ebec a Trois Rivi eres, Trois Rivie res, Qu ebec, G9A 5H7, Canada. E mail: jit uqtr.uquebec.ca. y Supported by NSERC Grant A4456 and by FCAR Grant 90 ER 0291. ....

J. W. Jaromczyk and G. T. Toussaint. Relative Neighborhood Graphs and Their Relatives. Proceedings of the IEEE, 80, 9, pp. 1502-1517, 1992.

....than its total length, needs being bounded by a factor f . In particular, every (strong) f spanner is a weak f spanner for some f at most as large as f , usually substantially smaller. Spanners for given P are most frequently computed by an obvious generalization of proximity graphs [17]: Partition space IR D into k 2 IN convex cones C 0 ; C k Gamma1 . Then, from vertex p 2P, draw directed edges (arcs) to the closest point u j of (p C j ) P; do this for j = 0 : k Gamma 1. The resulting graph is called a partitioned neighborhood graph (PNG) Its properties strongly ....

J.W. Jaromczyk and G.T. Toussaint: "Relative Neighborhood Graphs and Their Relatives", Proceedings of IEEE 80, 1992, 1502-1517.

....other at q; the corresponding graph is called the relative neighborhood graph [40] Figure 8 (a) shows a set S of points, Figure 8 (b) the corresponding Gabriel graph, and Figure 8 (c) its relative neighborhood graph. For a survey on proximity graphs and on their applications to graph drawing see [22] and [14] The Proximity Server of GS can generate infinitely many proximity graphs on a given set S. The user, through the canvas of the hypertextual interface, specifies both the set S and a nonnegative parameter fi. This parameter unambiguously defines the shape of the proximity region, called ....

J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 80(9):1502--1517, Sept. 1992.

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J. W. Jaromczyk and Godfried T. Toussaint. Relative neighborhood graphs and their relatives. Proceedings of the IEEE, 80(9):1502-1517, 1992.

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J. W. Jaromczyk and Godfried T. Toussaint. Relative neighborhood graphs and their relatives. Proceedings of the IEEE, 80(9):1502-1517, 1992.

....It is claimed in [105] that the resulting subset of fX; Y g is training set consistent. However, Toussaint [120] demonstrated a counter example. It should be noted that Tomek s preselected non consistent subset using the diametral sphere test implicitly computes a subgraph of the Gabriel graph [58] of fX; Y g, a graph admirably suited for condensing the training data that will be discussed later. 2.2 Order independent subsets CNN, RNN and Tomek s modi cation of CNN all have the undesirable property that the resulting reduced consistent subsets are a function of the order in which the ....

....For computing the RNG in d dimensions see Su and Chang [102] Proximity graphs have many applications in pattern recognition (see Toussaint [117] 124] 122] There is a vast literature on proximity graphs and it will not be reviewed here. The reader is directed to Jaromczyk and Toussaint [58] for a start. The most well known proximity graphs besides those mentioned above are the Gabriel graph GG and the Delaunay triangulation DT. All these are nested together in the following relationship: NNG MST RNG GG DT (1) 7.2 Decision boundary consistent subsets In 1978 Dasarathy and ....

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J. W. Jaromczyk and Godfried T. Toussaint. Relative neighborhood graphs and their relatives. Proceedings of the IEEE, 80(9):1502-1517, 1992.

....of the of the intersection of two circles with radii equal to d(p; q) centered at p and q, respectively. Notice that for any point x lying inside lune(p; q) we have that both d(x; p) d(p; q) and d(x; q) d(p; q) We now define an object known as the constrained relative neighborhood graph [5]. The relative neighborhood graph constrained to a set of line segments L, denoted as CRNG(L) is a graph defined in the following way. A node of CRNG(L) corresponds to an endpoint of a line segment in L. An edge exists between two nodes if and only if their corresponding endpoints e 1 and e 2 ....

J. JAROMCZYK AND G. TOUSSAINT. Relative neighborhood graphs and their relatives. Proceedings of the IEEE, 80, 9, pp. 1502-1517, 1992.

....closed disk that contains them; if the disk does not contain any other point of the set, the two points are connected by an edge. The resulting graph is known as the Gabriel Graph. For a comprehensive survey of proximity graphs on point sets, the reader is referred to Jaromczyk and Toussaint [JT92]. The study of proximity graphs defined on sets of disjoint line segments has received considerably less attention. Although for point sets the definition of proximity measures seems quite straightforward, this is no longer the case with line segments. For example, it seems natural that a ....

J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 80(9):1502--1517, September 1992.

.... outer structure (shape hull) Early approaches to this problem employed ad hoc heuristics. The first attempt to put such heuristics on a firm geometrical foundation was what I called the Gabriel hull in 1980 [58] The Gabriel hull of S is the boundary of the outer face of the Gabriel graph of S [36]. Since then there have been a score of improvements of this idea. A proximity graph on a set of points is a graph obtained by connecting two points in the set by an edge if the two points are close, in some sense, to each other. The minimum spanning tree (MST) the relative neighborhood graph ....

....obtained by connecting two points in the set by an edge if the two points are close, in some sense, to each other. The minimum spanning tree (MST) the relative neighborhood graph (RNG) the Gabriel graph, and the fi skeletons are proximity graphs that have been well investigated in this context [36]. Recently there has appeared a new proximity graph called the crust with some very interesting properties for shape analysis that should make it useful for application in practice [2] 26] For the most recent update of the most recent advances in this area see the column by O Rourke [47] In ....

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Jerzy W. Jaromczyk and Godfried T. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 80(9):1502--1517, September 1992.

....if all the remaining points in D lie outside the circle whose diameter is determined by (x, y) The reader can easily verify that this definition is equivalent to that in Fig. 1. In addition, if a Gabriel pair is connected by an edge, then the (now well known) Gabriel graph is obtained [MS80] [JT92] for which an O(n log n) time algorithm in the plane is now known and for which efficient expected time algorithms now exist in all dimensions using Voronoi diagrams [AB83] Au91] or heuristics [TBP84] The difference between the (complete) Gabriel graph of D and that computed in Fig. 1 is that ....

....away with CNN altogether. Whereas the algorithm of Tomek runs in at least O(n 3 ) time, the algorithm in [TBP84] runs in time closer to O(n 2 ) For more information concerning the efficient computation of other proximity graphs such as the relative neighborhood graph the reader is referred to [JT92]. 5. ....

Jaromczyk, J. W. and Toussaint, G. T., "Relative neighborhood graphs and their relatives, " Proc. IEEE, vol. 80, No. 9, September 1992, pp. 1502-1517.

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J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. Proceedings of the IEEE, 80:1502--1517, 1992.

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J. Jaromczyk, and G. Toussaint. Relative neighborhood graphs and their relatives. Proc. IEEE, 90:1502-1517, 1992.

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J.W. Jaromczyk and G.T. Toussaint, "Relative neighborhood graphs and their relatives," Proc. of IEEE, vol. 80, no. 9, pp. 1502--1517, 1992.

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J. W. Jaromczyk, G. T. Toussaint, Relative neighborhood graphs and their relatives, in: Proc. of the IEEE, Vol. 80, 1992, pp. 1502--1571. 2, 4

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J. W. Jaromczyk and Godfried T. Toussaint. Relative neighborhood graphs and their relatives. In Proc. IEEE, pages 1502-1517, 1992. 91

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J.W. Jaromczyk and G.T. Toussaint, "Relative neighborhood graphs and their relatives," Proc. of IEEE, vol. 80, no. 9, pp. 1502--1517, 1992.

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J. W. Jaromczyk and G. T. Toussaint. Relative neighborhood graphs and their relatives. ##### ####, 80:1502-1517, 1992.

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J.W. Jaromczyk and G.T. Toussaint, "Relative neighborhood graphs and their relatives," Proc. of IEEE, vol. 80, no. 9, pp. 1502--1517, 1992.

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J. Jaromczyk & G. Toussaint (1992), Relative neighborhood graphs and their relatives, Proc. IEEE 80, 1502--1517; CSA 0014664.

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Jerzy W. Jaromczyk and Godfried T. Toussaint, "Relative neighborhood graphs and their relatives," Proceedings IEEE, vol. 80, no. 9, pp. 1502--1517, September 1992.

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J. Jaromczyk and G. Toussaint. Relative neighborhood graphs and their relatives. Proc. of IEEE, 80(9):1502--1517, 1992.

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J. W. Jaromczyk and G. T. Toussaint, "Relative neighborhood graphs and their relatives," Proceedings of the IEEE, vol. 80, no. 9, pp. 1502--1517, 1992.

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J.W. Jaromczyk and G.T. Toussaint. Relative neighborhood graphs and their relatives. Proc. of IEEE, 80(9):1502--1517, 1992.

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Jaromczyk, J., Toussaint, G.: Relative neighborhood graphs and their relatives. Proceedings of IEEE 80 (1992) 1502--1517

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J. Jaromczyk and G. Toussaint. Relative neighborhood graphs and their relatives. Proceedings of the IEEE, 80:1502-1517, 1992.

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J.W. Jaromczyk and G.T. Toussaint, \Relative neighborhood graphs and their relatives," Proceedings of IEEE, vol. 80, no. 9, pp. 1502-1517, 1992.

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Jaromczyk, J., Toussaint, G.: Relative neighborhood graphs and their relatives. Proceedings of IEEE 80 (1992) 1502-1517

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J. W. Jaromczyk and G. T. Toussaint. Relative Neighborhood Graphs and Their Relatives. Proc. IEEE, 80(9):1502--1517, September 1992. 2

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