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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.  ...  In this paper we are interested in solving the full-query version of the minimum link distance problem in a special class of rectilinear polygons.  ... 
doi:10.1016/0304-3975(94)00195-o fatcat:qabjfilibzba5putolubcqvpq4

Page 1120 of Mathematical Reviews Vol. , Issue 96b [page]

1996 Mathematical Reviews  
(Sridhar, Radhakrishnan] (1-OK-C; Norman, OK); Han, K. (1-OK-C; Norman, OK); Chandrasekharan, N. (1-LYLCH; Chicago, IL) Efficient algorithms for shortest distance queries on special classes of polygons  ...  In this paper, we present efficient algorithms to solve the query version of the RMBP problem for special classes of rectilinear polygons given their visibility graphs.  ... 

Walking your dog in the woods in polynomial time

Erin Wolf Chambers, Éric Colin de Verdière, Jeff Erickson, Sylvain Lazard, Francis Lazarus, Shripad Thite
2008 Proceedings of the twenty-fourth annual symposium on Computational geometry - SCG '08  
We describe a polynomial-time algorithm to compute the homotopic Fréchet distance between two given polygonal curves in the plane minus a given set of obstacles, which are either points or polygons.  ...  The Fréchet distance between two curves in the plane is the minimum length of a leash that allows a dog and its owner to walk along their respective curves, from one end to the other, without backtracking  ...  We present a polynomial-time algorithm for a special case of this problem, which is to compute the homotopic Fréchet distance between two polygonal curves in the plane minus a set of point or polygonal  ... 
doi:10.1145/1377676.1377694 dblp:conf/compgeom/ChambersVELLT08 fatcat:b7kuo5qnrrbwrn2n5iz7gtsndu

Page 7123 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
Davis, Parallelizing an algorithm for visibility on polyhedral terrain (75-84); Yi-Jen Chiang and Roberto Tamassia, Optimal shortest path and minimum-link path queries between two convex polygons inside  ...  In fact, we provide the first worst-case optimal (O(nlogn) time, O(n) space) algorithm that is valid for the full class of what have been called nice metrics in the plane.  ... 

Page 1606 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
Summary: “We describe a new data structure for answering shortest path queries inside a simple polygon.  ...  {For the entire collection see MR 92b:68019.} 92c:68190 68U05 68P05 Hershberger, John (1-DECSY) A new data structure for shortest path queries in a simple polygon. Inform. Process.  ... 

Homotopic Fréchet distance between curves or, walking your dog in the woods in polynomial time

Erin Wolf Chambers, Éric Colin de Verdière, Jeff Erickson, Sylvain Lazard, Francis Lazarus, Shripad Thite
2010 Computational geometry  
We describe a polynomial-time algorithm to compute the homotopic Fréchet distance between two given polygonal curves in the plane minus a given set of polygonal obstacles.  ...  The Fréchet distance between two curves in the plane is the minimum length of a leash that allows a dog and its owner to walk along their respective curves, from one end to the other, without backtracking  ...  We would like to thank the anonymous referees for their careful reading of the paper and their numerous suggestions for improvement.  ... 
doi:10.1016/j.comgeo.2009.02.008 fatcat:vqtemc2z6nffxd7si62be32s7u

Page 5145 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
First, we present a data structure using O(nlog n) storage such that a shortest path between two query points can be computed efficiently.  ...  images, for a large class of object types (e.g., points,  ... 

Indexing Network Voronoi Diagrams [chapter]

Ugur Demiryurek, Cyrus Shahabi
2012 Lecture Notes in Computer Science  
Although the existing approaches successfully utilize the network Voronoi diagram as a way to partition the space for their specific problems, there is little emphasis on how to efficiently find and access  ...  The Network Voronoi diagram and its variants have been extensively used in the context of numerous applications in road networks, particularly to efficiently evaluate various spatial proximity queries  ...  In [19] , Samet et al. proposed shortest path quadtree algorithm for efficient evaluation of both shortest path and kNN queries in road networks.  ... 
doi:10.1007/978-3-642-29038-1_38 fatcat:c7iwcvhyx5erxb23eyfirb2kq4

Computing external farthest neighbors for a simple polygon

Pankaj K. Agarwal, Alok Aggarwal, Boris Aronov, S.Rao Kosaraju, Baruch Schieber, Subhash Suri
1991 Discrete Applied Mathematics  
For a vertex p of Y, let @J(P) be the set of points on :sP that are farthest fromp, where the distance between two points is the length of the (Euclidean) shortest path that connects them without intersecting  ...  Suri, Computing external farthest neighbors for a simple polygon, Discrete Applied Mathematics 31 (1991) 97-l 11. Let .+' be (the boundary of) a simple polygon with n vertices.  ...  In Section 3 we prove some properties of external shortest paths, which lead us to an efficient algorithm for computing the external farthest neighbors for every vertex of the polygon.  ... 
doi:10.1016/0166-218x(91)90063-3 fatcat:klzdgk6rlbbjzhc2dx3u6cnotq

Polygonal path simplification with angle constraints

Danny Z. Chen, Ovidiu Daescu, John Hershberger, Peter M. Kogge, Ningfang Mi, Jack Snoeyink
2005 Computational geometry  
We present efficient geometric algorithms for simplifying polygonal paths in R 2 and R 3 that have angle constraints, improving by nearly a linear factor over the graph-theoretic solutions based on known  ...  The algorithms we present match the time bounds for their unconstrained counterparts.  ...  Acknowledgement The authors would like to thank the anonymous reviewers for their helpful comments and suggestions.  ... 
doi:10.1016/j.comgeo.2004.09.003 fatcat:6xnshgwedvc7daebcvwjfphifa

Page 7483 of Mathematical Reviews Vol. , Issue 94m [page]

1994 Mathematical Reviews  
Our algorithm takes O(n log? n) preprocessing time, O(n log” n) space and O(log” n) query time for the distance problem.  ...  {For the entire collection see MR 94i:68003.} 94m:68194 68U05 52B55 Yan, Yong (PRC-HUST-C; Wuhan) An optimal algorithm for solving collision distance between convex polygons in plane.  ... 

Page 3242 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
The paper investigates a special class of such scale spaces for three- dimensional images.  ...  Summary: “We give a subquadratic (O(n*/***) time and O(n) space) algorithm for computing Euclidean shortest paths in the plane in the presence of polygonal obstacles; previous time bounds were at least  ... 

Shortest path problem in rectangular complexes of global nonpositive curvature

Victor Chepoi, Daniela Maftuleac
2013 Computational geometry  
In this paper, we present an efficient algorithm for answering two-point distance queries in CAT(0) rectangular complexes and two of theirs subclasses, ramified rectilinear polygons (CAT(0) rectangular  ...  If K is a ramified rectilinear polygon, then one can construct a data structure D of optimal size O(n) and answer two-point shortest path queries in O(d(p,q)logΔ) time, where Δ is the maximal degree of  ...  In this paper, we present an algorithm for efficiently solving two-point shortest path queries in CAT(0) rectangular complexes, i.e., rectangular complexes of global non-positive curvature.  ... 
doi:10.1016/j.comgeo.2012.04.002 fatcat:75aglel2izhzjat2uqsq74pg5e

Efficient Max-Norm Distance Computation and Reliable Voxelization [article]

Gokul Varadhan, Shankar Krishnan, Young J. Kim, Suhas Diggavi, Dinesh Manocha
2003 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
We present techniques to efficiently compute the distance under max-norm between a point and a wide class of geometric primitives.  ...  We formulate the distance computation as an optimization problem and use this framework to design efficient algorithms for convex polytopes, algebraic primitives and triangulated models.  ...  We thank Kenny Hoff for his HAVOC software, Joe Warren and Scott Schaefer for providing us with dual contouring code, and the reviewers for their feedback and suggestions.  ... 
doi:10.2312/sgp/sgp03/116-126 fatcat:pk52og4wovcjpgmw2yyncjtopi

Computational Geometry Column 42 [article]

Joseph S. B. Mitchell, Joseph O'Rourke
2001 arXiv   pre-print
A compendium of thirty previously published open problems in computational geometry is presented.  ...  We are grateful to Erik Demaine for several helpful comments.  ...  Relatedly, is there a simple linear-time algorithm for computing a shortest path in a simple polygon, without first applying a more complicated triangulation algorithm? 11.  ... 
arXiv:cs/0108021v1 fatcat:xgoxckdbl5a7hacx54drwifute
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