P. Bose, M. McAllister, and J. Snoeyink. Optimal algorithms to embed trees in a point set. Journal of Graph Algorithms and Applications, 1(2):1--15, 1997. A preliminary version appeared in Graph Drawing (Proc. GD '95), LNCS 1027, pg. 64--75.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Originally, the problem was how to map a given tree T of n vertices at a given set of points S in the plane such that the edges can be drawn straightline and without any crossings. Variants of this problem have been explored, either with or without keeping the position of one specific node fixed [16, 12, 2]. Generalizing the graph class, but still using the required straightline planar drawing, Gritzmann et al. 11] gave an elegant divide and conquer scheme to partition the point set and the set of vertices simultaneously. They showed that using this mapping outerplanar graphs can be drawn without ....

Bose, P., M. McAllister, and J. Snoeyink. Optimal algorithms to embed trees in a point set. Journal of Graph Algorithms and Applications 1998.

....Originally, the problem was how to map a given tree T of n vertices at a given set of points S in the plane such that the edges can be drawn straightline and without any crossings. Variants of this problem have been explored, either with or without keeping the position of one speci c node xed [13, 10, 2] Generalizing the graph class, but still using the required straightline planar drawing, Gritzmann et al. 9] proved that outerplanar graphs can be drawn without any bends. In the consequent papers [3] and [1] ecient implementations have been developed. The latest result in [1] is an O(n log ....

Bose, P., M. McAllister, and J. Snoeyink. Optimal algorithms to embed trees in a point set. Journal of Graph Algorithms and Applications 1998.

.... Aronov, Seidel and Souvaine [1] and Kranakis and Urrutia [5] studied the problem of finding common triangulations of point sets of polygons; see also Shapira and Rappaport [7] The problem of finding embeddings of trees on point sets has also been studied recently by Bose, McAllister and Snoeyink [2], Ibeke, Perles, Tamura and Tokunaga [4] Let P n and Q n be labeled point sets, both labeled with the integers 1; n. A nonintersecting path (henceforth called path) of P n is a non repeating sequence of points i 1 ; i k such that the polygonal path obtained by connecting i j to ....

P. Bose, M. McAllister, and J. Snoeyink, "Optimal algorithms to embed trees in a point set", in proceedings of Symposium on Graph Drawing, GD'95, Passau Germany, September 1995, F. J. Brandenburg (Ed.), Springer Verlag Lecture Notes in Computer Science, pp. 64-75, vol. 1027, 1995.

....P of n points in the plane, we present an O(n log n) time and O(n) space algorithm to compute a straight line embedding of G in P , improving upon the algorithm in [GMPP91, CU96] that requires O(n ) time. Our algorithm is near optimal as there is an n log n) lower bound for the problem [BMS95]. We present a simpler O(nd) time and O(n) space algorithm to compute a straight line embedding of G in P where log n d 2n is the length of the longest vertex disjoint path in the dual of G. Therefore, the time complexity of the simpler algorithm varies between O(n log n) and O(n ....

....it could if p was not the deepest point of P , obtained by repeatedly discarding points on the convex hull. Subsequently, Ikebe et. al [IPTT94] showed that there was always such an embedding using a quadratic time algorithm. In fact, all three algorithms use quadratic time. Finally, Bose et. al [BMS95] proved an n log n) lower bound for the problem and provided a matching O(n log n) time embedding algorithm. With the embedding problem being resolved when the input graphs are restricted to trees and unresolved when the input graphs are planar, a natural question to ask is what is the largest ....

[Article contains additional citation context not shown here]

P. Bose, M. McAllister, and J. Snoeyink. Optimal algorithms to embed trees in a point set. Journal of Graph Algorithms and Applications, to appear. Also appears in Proceedings of Graph Drawing GD'95, LNCS 1027, pp. 64-75, 1995.

....points in the plane, we present an O(n log n) time and O(n) space algorithm to compute a straight line embedding of G in P , improving upon the algorithm in [GMPP91, CU96] that requires O(n ) time. Our algorithm is near optimal as there is an Omega (n log n) lower bound for the problem [BMS95]. We present a simpler O(nd) time and O(n) space algorithm to compute a straight line embedding of G in P where log n d 2n is the length of the longest vertex disjoint path in the dual of G. Therefore, the time complexity of the simpler algorithm varies between O(n log n) and O(n ) ....

....it could if p was not the deepest point of P , obtained by repeatedly discarding points on the convex hull. Subsequently, Ikebe et. al [IPTT94] showed that there was always such an embedding using a quadratic time algorithm. In fact, all three algorithms use quadratic time. Finally, Bose et. al [BMS95] proved an Omega lower bound for the problem and provided a matching O(n log n) time embedding algorithm. With the embedding problem being resolved when the input graphs are restricted to trees and unresolved when the input graphs are planar, a natural question to ask is what is the largest ....

[Article contains additional citation context not shown here]

P. Bose, M. McAllister, and J. Snoeyink. Optimal algorithms to embed trees in a point set. Journal of Graph Algorithms and Applications, to appear. Also appears in Proceedings of Graph Drawing GD'95, LNCS 1027, pp. 64--75, 1995.

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P. Bose, M. McAllister, and J. Snoeyink. Optimal algorithms to embed trees in a point set. Journal of Graph Algorithms and Applications, 1(2):1--15, 1997. A preliminary version appeared in Graph Drawing (Proc. GD '95), LNCS 1027, pg. 64--75.

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