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Efficient algorithms for shortest distance queries on special classes of polygons

1995
*
Theoretical Computer Science
*

In this paper, we present

doi:10.1016/0304-3975(94)00195-o
fatcat:qabjfilibzba5putolubcqvpq4
*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*. ...##
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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

2008
*
Proceedings of the twenty-fourth annual symposium on Computational geometry - SCG '08
*

We describe a polynomial-time

doi:10.1145/1377676.1377694
dblp:conf/compgeom/ChambersVELLT08
fatcat:b7kuo5qnrrbwrn2n5iz7gtsndu
*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*...##
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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. ...##
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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

2010
*
Computational geometry
*

We describe a polynomial-time

doi:10.1016/j.comgeo.2009.02.008
fatcat:vqtemc2z6nffxd7si62be32s7u
*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. ...##
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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]

2012
*
Lecture Notes in Computer Science
*

Although the existing approaches successfully utilize the network Voronoi diagram as a way to partition the space

doi:10.1007/978-3-642-29038-1_38
fatcat:c7iwcvhyx5erxb23eyfirb2kq4
*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. ...##
###
Computing external farthest neighbors for a simple polygon

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*. ...

##
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Polygonal path simplification with angle constraints

2005
*
Computational geometry
*

We present

doi:10.1016/j.comgeo.2004.09.003
fatcat:6xnshgwedvc7daebcvwjfphifa
*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. ...##
###
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

2013
*
Computational geometry
*

In this paper, we present an

doi:10.1016/j.comgeo.2012.04.002
fatcat:75aglel2izhzjat2uqsq74pg5e
*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. ...##
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Efficient Max-Norm Distance Computation and Reliable Voxelization
[article]

2003
*
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
*

We present techniques to

doi:10.2312/sgp/sgp03/116-126
fatcat:pk52og4wovcjpgmw2yyncjtopi
*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. ...##
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Computational Geometry Column 42
[article]

2001
*
arXiv
*
pre-print

A compendium

arXiv:cs/0108021v1
fatcat:xgoxckdbl5a7hacx54drwifute
*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. ...
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