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There is a unique crossingminimal rectilinear drawing of K18
"... We show that, up to isomorphism, there is a unique crossingminimal rectilinear drawing of K18. As a consequence we settle, in the negative, the following question from Aichholzer and Krasser: does there always exist an crossingminimal drawing of Kn that contains a crossingminimal drawing of Kn−1? ..."
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We show that, up to isomorphism, there is a unique crossingminimal rectilinear drawing of K18. As a consequence we settle, in the negative, the following question from Aichholzer and Krasser: does there always exist an crossingminimal drawing of Kn that contains a crossingminimal drawing of Kn−1
Mathematical Programming Formulation of Rectilinear Crossing Minimization
, 2002
"... In a rectilinear drawing of a simple graph G each vertex is mapped to a distinct point in the plane and each edge is represented by a straightline segment with appropriate ends. The goal of rectilinear crossing minimization is to find a rectilinear drawing of G with as few edge crossings as possibl ..."
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In a rectilinear drawing of a simple graph G each vertex is mapped to a distinct point in the plane and each edge is represented by a straightline segment with appropriate ends. The goal of rectilinear crossing minimization is to find a rectilinear drawing of G with as few edge crossings
A lower bound for the rectilinear crossing number
 Graphs and Combinatorics
, 2003
"... We give a new lower bound for the rectilinear crossing number cr(n) of the complete geometric graph Kn. Weprovethatcr(n) ≥ 1 ¥ ¦ ¥ ¦ ¥ ¦ ¥ ¦ n n−1 n−2 n−3 andweextendtheproofof ..."
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Cited by 30 (10 self)
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We give a new lower bound for the rectilinear crossing number cr(n) of the complete geometric graph Kn. Weprovethatcr(n) ≥ 1 ¥ ¦ ¥ ¦ ¥ ¦ ¥ ¦ n n−1 n−2 n−3 andweextendtheproofof
A Heuristic Algorithm for the Rectilinear Steiner Arborescence Problem
 Engineering Optimization
, 1994
"... In this paper the following problem is considered: given a root node R in a mesh and a set D of nodes from the mesh, construct a shortestpath tree rooted at R that spans the set D and minimizes the number of links used. The problem is equivalent as finding a Steiner tree in a directed mesh in whic ..."
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Cited by 6 (0 self)
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in which all the links point away from the root node R. The problem of finding a Steiner tree in such grid has been known in the literature as the Rectilinear Steiner Arborescence (RSA) problem. Rao et. al [9] have proposed an efficient heuristic algorithm for a special case of this problem, in which all
ON THE COMPLEXITY OF SOME COMMON GEOMETRIC LOCATION PROBLEMS
 SIAM J. COMPUTING
, 1984
"... Given n demand points in the plane, the pcenter problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demo & point to its respective nearest supply point. The pmedian problem is to minimize the sum of distances from demand points to their resp ..."
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Cited by 140 (1 self)
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Given n demand points in the plane, the pcenter problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demo & point to its respective nearest supply point. The pmedian problem is to minimize the sum of distances from demand points
Efficient Rectilinear Steiner Tree Construction with Rectilinear Blockages
 Proc. ICCD
, 2005
"... Given n points on a plane, a Rectilinear Steiner Minimal Tree (RSMT) connects these points through some extra points called steiner points to achieve a tree with minimal total wire length. Taking blockages into account dramatically increases the problem complexity. It is extremely unlikely that an e ..."
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Cited by 16 (2 self)
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Given n points on a plane, a Rectilinear Steiner Minimal Tree (RSMT) connects these points through some extra points called steiner points to achieve a tree with minimal total wire length. Taking blockages into account dramatically increases the problem complexity. It is extremely unlikely
Compressing rectilinear pictures and minimizing access control lists
 In Proceedings of the Proceedings of ACMSIAM Symposium on Discrete Algorithms (SODA
, 2007
"... We consider a geometric model for the problem of minimizing access control lists (ACLs) in network routers, a model that also has applications to rectilinear picture compression and figure drawing in common graphics software packages. Here the goal is to create a colored rectilinear pattern within a ..."
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Cited by 27 (1 self)
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We consider a geometric model for the problem of minimizing access control lists (ACLs) in network routers, a model that also has applications to rectilinear picture compression and figure drawing in common graphics software packages. Here the goal is to create a colored rectilinear pattern within
The Polygonal Contraction Heuristic for Rectilinear Steiner Tree Construction
, 2005
"... Motivated by VLSI/ULSI routing applications, we present a heuristic for rectilinear Steiner minimal tree (RSMT) construction. We transform a rectilinear minimum spanning tree (RMST) into an RSMT by a novel method called polygonal contraction. Experimental results show that the heuristic matches or e ..."
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Motivated by VLSI/ULSI routing applications, we present a heuristic for rectilinear Steiner minimal tree (RSMT) construction. We transform a rectilinear minimum spanning tree (RMST) into an RSMT by a novel method called polygonal contraction. Experimental results show that the heuristic matches
Homotopic rectilinear routing with few links and thick edges
 Proc. LATIN 2010, volume 6034 of Lecture Notes Comput. Sci
, 2010
"... We study the problem of finding noncrossing thick minimumlink rectilinear paths homotopic to a set of input paths in an environment with rectangular obstacles. This problem occurs in the context of map schematization under geometric embedding restrictions, for example, when schematizing a highwa ..."
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Cited by 1 (0 self)
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We study the problem of finding noncrossing thick minimumlink rectilinear paths homotopic to a set of input paths in an environment with rectangular obstacles. This problem occurs in the context of map schematization under geometric embedding restrictions, for example, when schematizing a high
Compressing Rectilinear Pictures and Minimizing Access Control Lists
"... We consider a geometric model for the problem of minimizing access control lists (ACLs) in network routers, a model that also has applications to rectilinear picture compression and figure drawing in common graphics software packages. Here the goal is to create a colored rectilinear pattern within a ..."
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We consider a geometric model for the problem of minimizing access control lists (ACLs) in network routers, a model that also has applications to rectilinear picture compression and figure drawing in common graphics software packages. Here the goal is to create a colored rectilinear pattern within
Results 1  10
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