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Optimal parallel algorithms for rectilinear link-distance problems

A. Lingas, A. Maheshwari, J. R. Sack
1995 Algorithmica  
We provide optimal parallel solutions to several link distance problems set in trapezoided rectilinear polygons.  ...  We develop techniques for solving link distance problems in parallel which are expected to nd applications in the design of other parallel computational geometry algorithms.  ...  Acknowledgements : Authors gratefully acknowledge Torben Hagerup for suggesting an improvement of the diameter algorithm over an earlier version of this paper.  ... 
doi:10.1007/bf01206332 fatcat:kal5bv4mazbiddaizbg2b5lmju

k-Link Rectilinear Shortest Paths Among Rectilinear Obstacles in the Plane

Valentin Polishchuk, Joseph S. B. Mitchell
2005 Canadian Conference on Computational Geometry  
We present an algorithm for computing k-link rectilinear shortest paths among rectilinear obstacles in the plane.  ...  Our algorithm runs in time O(kn log 2 n) and space O(kn), where n is the number of vertices of the obstacles. Previous algorithms for the problem had worst-case time complexity O(kn 2 ).  ...  In rectilinear polygonal domains, efficient algorithms are known for the bi-criteria path problem that combines rectilinear link distance and L 1 length.  ... 
dblp:conf/cccg/PolishchukM05 fatcat:wxvsm3f4o5dy3movkc72zhv4li

Page 5146 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
(D-FRBG-I); Schuierer, Sven (D-FRBG-I) An optimal algorithm for the rectilinear link center of a rectilinear polygon.  ...  As a consequence we also obtain a linear time solution for the rectilinear link radius problem. To our knowledge this is the first optimal algorithm which solves a nontrivial center problem.”  ... 

Page 4362 of Mathematical Reviews Vol. , Issue 96g [page]

1996 Mathematical Reviews  
We develop techniques for solving link-distance problems in parallel which are expected to find applications in the design of other parallel computational geometry algorithms.  ...  We employ these parallel techniques, for example, to compute (on a CREW PRAM) optimally the link di- ameter, the link center, and the central diagonal of a rectilinear polygon.” 96g:68142 68U05 68Q25 Maryukov  ... 

Page 5114 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
In this paper we present optimal sequential and parallel algorithms to compute a minimum rectilinear link path in a trapezoided region R.  ...  {For the entire collection see MR 2000¢:68006. } 2000g:68153 68U05 Maheshwari, Anil (3-CARL-SC; Ottawa, ON); Sack, Jorg-Riidiger (3-CARL-SC; Ottawa, ON) Simple optimal algorithms for rectilinear link path  ... 

Page 6523 of Mathematical Reviews Vol. , Issue 98J [page]

1998 Mathematical Reviews  
We propose an algorithm for this problem that requires at most m + | links to reach from s to 1, where m denotes the rectilinear link distance between s and 1 in P.  ...  To our knowledge, this problem has not been studied before We present an algorithm for this problem that requires at most 2m — 1 links to reach from s to ¢, where m denotes the link distance between s  ... 

Page 1215 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
; Freiburg) An optimal data structure for shortest rectilinear path queries in a simple rectilinear polygon.  ...  In this paper, efficient algorithms are given for several generalized problems involving objects that are not necessarily iso-oriented.  ... 

On rectilinear link distance

Mark de Berg
1991 Computational geometry  
In this paper we study two link distance problems for rectilinear paths inside a simple rectilinear polygon P.  ...  The resulting path is not only optimal in the rectilinear link metric, but it is optimal in the L,-metric as well.  ...  Acknowledgement I would like to thank Mark Overmars for his many helpful comments, which improved the contents of this paper considerably.  ... 
doi:10.1016/0925-7721(91)90010-c fatcat:nxhntuxtz5hghgzdeu6krznw2i

On Covering Points with Minimum Turns

Minghui Jiang
2015 International journal of computational geometry and applications  
Axis-parallel Lines For the rectilinear version of the problem in which the lines must be axis-parallel, • Hassin and Megiddo (1991) observed that the problem in R 2 reduces to vertex cover in bipartite  ...  Hyperplanes For the more general problem of covering n points in R d by k (not necessarily axis-parallel) hyperplanes, • Langerman and Morin (2005) presented FPT algorithms with both d and k as parameters  ...  et al. (2009)'s constructive proof for a related combinatorial bound implies an approximation algorithm for Minimum-Link Rectilinear Spanning Path that uses at most 1 more turn than the optimal.  ... 
doi:10.1142/s0218195915500016 fatcat:doe4blchxjagzc65r3ragl6zxu

On Covering Points with Minimum Turns [chapter]

Minghui Jiang
2012 Lecture Notes in Computer Science  
et al. (2009)'s constructive proof for a related combinatorial bound implies an approximation algorithm for Minimum-Link Rectilinear Spanning Path that uses at most 1 more turn than the optimal.  ...  Interestingly, for this simplest case, • Stein and Wagner (2001) presented an approximation algorithm for Minimum-Link Rectilinear Covering Tour that uses at most 2 more turns than the optimal, • Bereg  ...  Concluding Remarks While we have pointed out mistakes in several previous algorithms for k-Link Rectilinear Covering Tour and its variants in R 2 , we still believe that these problems are most likely  ... 
doi:10.1007/978-3-642-29700-7_6 fatcat:ockwpdbeyrf2ze4f4zl6t6ki7e

Optimal on-line algorithms for walking with minimum number of turns in unknown streets

Subir Kumar Ghosh, Sanjeev Saluja
1997 Computational geometry  
We propose an algorithm for this problem that requires at most m + 1 links to reach from s to t, where m denotes the rectilinear link distance between s and t in P.  ...  We present an algorithm for this problem that requires at most 2m -1 links to reach from s to t, where m denotes the link distance between s and t in P.  ...  Pijush Ghosh for his valuable suggestions.  ... 
doi:10.1016/s0925-7721(97)00003-5 fatcat:6didxk3n3be37fpzx5cotf4uha

An O(n5/2logn) algorithm for the Rectilinear Minimum Link-Distance Problem in three dimensions

David P. Wagner, Robert Scot Drysdale, Clifford Stein
2009 Computational geometry  
In this paper we consider the Rectilinear Minimum Link Path Problem among rectilinear obstacles in three dimensions.  ...  Previously known algorithms have had worst-case running times of (n 3 ).  ...  We are also grateful to Kyung-Yong Chwa for the contribution of his lab space at Korea Advanced Institute for Science and Technology (KAIST) in which early versions of this paper were written.  ... 
doi:10.1016/j.comgeo.2008.04.006 fatcat:isosy2oc5fbkfhic5oinzugzyi

Efficient algorithms for shortest distance queries on special classes of polygons

R. Sridhar, K. Han, N. Chandrasekharan
1995 Theoretical Computer Science  
In this paper, we present efficient algorithms to solve the query version of the RMBP problem for special classes of rectilinear polygons given their oisibility graphs.  ...  For the case of a chordal graph G, our algorithms give a distance which is at most one away from the actual shortest distance.  ...  The minimum link distance problem given a pair of points in the plane asks for a path that minimizes the link distance. Arkin et al.  ... 
doi:10.1016/0304-3975(94)00195-o fatcat:qabjfilibzba5putolubcqvpq4

An optimal parallel algorithm using exclusive read/writes for the rectilinear Voronoi diagram

Sumanta Guha
1993 Computational geometry  
., An optimal parallel algorithm using exclusive read/writes for the rectilinear Voronoi diagram, Computational Geometry: Theory and Applications 3 (1993) 37-52.  ...  We present the first optimal parallel algorithm to compute the Voronoi diagram in the rectilinear (I", Manhattan) metric.  ...  Acknowledgements I would like to thank my thesis advisor Quentin Stout for many helpful discussions and Phil MacKenzie for pointing out some important references.  ... 
doi:10.1016/0925-7721(93)90029-6 fatcat:sfruialoindxfflkgry2nbqice

NP-completeness and FPT Results for Rectilinear Covering Problems

Apichat Heednacram, Francis Suraweera, Vladimir Estivill-Castro
2010 Journal of universal computer science (Online)  
This paper discusses three rectilinear (that is, axis-parallel) covering problems in d dimensions and their variants.  ...  We provide the proof that the Rectilinear Minimum Link Traveling Salesman Problem and the Rectilinear Minimum Link Spanning Path Problem are NP-complete by a reduction from the One-In-Three 3-SAT problem  ...  Acknowledgments We thank the anonymous reviewers for valuable remarks that improved the original version of this paper.  ... 
doi:10.3217/jucs-016-05-0622 dblp:journals/jucs/Estivill-CastroHS10 fatcat:s6rnnd5vhjafnlnpwm4adpihga
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