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Connecting the maximum number of grid nodes to the boundary with non-intersecting line segments

  • Leonidas Palios
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 824)

Abstract

We consider the problem of finding the maximum number of nodes in a grid (from a given set of such nodes) that can be connected to the boundary of the grid by means of non-intersecting line segments parallel to the grid axes. The work is motivated from the VLSI/WSI array processor technology, and in particular, the single-track switch model for configurable array processors ([4]). The problem has been investigated by Bruck and Roychowdhury, who described an algorithm to find the maximum number of compatible connections of n given nodes in the grid in O(n3) time and O(n2) space ([2]). In this paper, we present methods that take advantage of the dependency of similar configurations and enable us to resolve the problem in O(n2log n) time and O(n2) space; instrumental in our algorithm is the use of a new type of priority search trees which is of interest in its own right.

Keywords

Line Segment Array Processor Connection Pattern Grid Boundary Dummy Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Y. Birk and J.B. Lotspiech, “A Fast Algorithm for Connecting Grid Points to the Boundary with Nonintersecting Straight Lines,” Proc. 2nd Annual Symp. on Discrete Algorithms (1991), 465–474.Google Scholar
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    J. Bruck and V.P. Roychowdhury, “How to Play Bowling in Parallel on the Grid,” Journal of Algorithms12 (1991), 516–529.Google Scholar
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    E.M. McCreight, “Priority Search Trees,” SIAM Journal on Computing14 (1985), 257–276.MathSciNetGoogle Scholar
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    L. Palios, “Connecting Grid Points to the Boundary of the Grid by Means of Non-intersecting Line Segments,” Report GCG56, The Geometry Center, 1993.Google Scholar
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    V.P. Roychowdhury and J. Bruck, “On Finding Non-intersecting Paths in Grids and its Application in Reconfiguring VLSI/WSI Arrays,” Proc. 1st Annual Symp. on Discrete Algorithms (1990).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Leonidas Palios
    • 1
  1. 1.The Geometry CenterUniv. of MinnesotaUSA

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