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On Contact Graphs with Cubes and Proportional Boxes
[chapter]

2016
*
Lecture Notes in Computer Science
*

We study two variants

doi:10.1007/978-3-662-49192-8_9
fatcat:ccqlcjhr4bajbf6swcllnwnfzu
*of**the*problem*of*contact representation*of**planar*graphs with axis-aligned boxes. ... We show how to construct such representations representation for some classes*of**planar*graphs. ... If G is*planar*, then it is called a*planar*3-*tree*. A plane 3-*tree*is a*planar*3-*tree*along with a fixed*planar*embedding. ...##
###
Fine-Grained Location-Free Planarization in Wireless Sensor Networks

2013
*
IEEE Transactions on Mobile Computing
*

*The*

*planar*topologies constructed by current location-free methods often have large

*stretch*factors. ...

*The*simulation results show that our method produces high-quality

*planar*graphs with a small

*stretch*factor in practical large-scale networks. ... ACKNOWLEDGMENTS

*The*authors are grateful for a variety

*of*valuable comments from

*the*anonymous reviewers. Dezun Dong ...

##
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Fine-grained location-free planarization in wireless sensor networks

2011
*
2011 Proceedings IEEE INFOCOM
*

*The*

*planar*topologies constructed by current location-free methods often have large

*stretch*factors. ...

*The*simulation results show that our method produces high-quality

*planar*graphs with a small

*stretch*factor in practical large-scale networks. ... ACKNOWLEDGMENTS

*The*authors are grateful for a variety

*of*valuable comments from

*the*anonymous reviewers. Dezun Dong ...

##
###
Intersection graphs of L-shapes and segments in the plane

2016
*
Discrete Applied Mathematics
*

any format or medium without

doi:10.1016/j.dam.2016.01.028
fatcat:t7z7jvn6anfrlor4ar6v5lfese
*the*formal permission*of**the*copyright holders. ... provided that: • a full bibliographic reference is made to*the*original source • a link is made to*the*metadata record in DRO •*the*full-text is not changed in any way*The*full-text must not be sold in ... Here we give an easy proof for a non-trivial subclass*of**planar*graphs, namely*planar*3-*trees*. A 3-*tree*is an edge-maximal graph*of*treewidth 3. ...##
###
Intersection Graphs of L-Shapes and Segments in the Plane
[chapter]

2014
*
Lecture Notes in Computer Science
*

any format or medium without

doi:10.1007/978-3-662-44465-8_26
fatcat:7vaqzk7xyjbl3aiqpcyb6guhuu
*the*formal permission*of**the*copyright holders. ... provided that: • a full bibliographic reference is made to*the*original source • a link is made to*the*metadata record in DRO •*the*full-text is not changed in any way*The*full-text must not be sold in ... Here we give an easy proof for a non-trivial subclass*of**planar*graphs, namely*planar*3-*trees*. A 3-*tree*is an edge-maximal graph*of*treewidth 3. ...##
###
1-String B_1-VPG Representations of Planar Partial 3-Trees and Some Subclasses
[article]

2015
*
arXiv
*
pre-print

We also that some subclasses

arXiv:1506.07246v1
fatcat:63yszsx7cffvbdovftwgb43yey
*of**planar*partial 3-*trees*have L-representations, i.e., a B_1-VPG representation where every curve has*the**shape**of*an L. ...*Planar*partial 3-*trees*are subgraphs*of*those*planar*graphs obtained by repeatedly inserting a vertex*of*degree 3 into a face. ... However, for some subclasses*of**planar*partial 3-*trees*, we can show that fewer*shapes*suffice. ...##
###
Intersection Graphs of L-Shapes and Segments in the Plane
[article]

2016
*
arXiv
*
pre-print

We show that all

arXiv:1405.1476v2
fatcat:ekp6twulfrcmpa56wbu2bn6aqe
*planar*3-*trees*, all line graphs*of**planar*graphs, and all full subdivisions*of**planar*graphs are {L}-graphs. ... An L-*shape*is*the*union*of*a horizontal and a vertical segment with a common endpoint. These come in four rotations: L, Γ, LE and . ... Is there a parameter*of*SEG-graphs or SEGrepresentations ensuring few bends in their VPG-representations? It is known that*the*number*of*slopes in*the*SEG-representation is not*the*right answer [6] . ...##
###
1-string B1-VPG-representations of planar partial 3-trees and some subclasses

2015
*
Canadian Conference on Computational Geometry
*

We also show that some subclasses

dblp:conf/cccg/BiedlD15
fatcat:egiwopn7vvh6hc7p7e5ye5qsoy
*of**planar*partial 3-*trees*have {L}representations, i.e., a B 1 -VPG representation where every curve has*the**shape**of*an L. ...*Planar*partial 3-*trees*are subgraphs*of*those*planar*graphs obtained by repeatedly inserting a vertex*of*degree 3 into a face. ... However, for some subclasses*of**planar*partial 3-*trees*, we can show that fewer*shapes*suffice. ...##
###
Advances in the theory and practice of graph drawing

1999
*
Theoretical Computer Science
*

Foremost among

doi:10.1016/s0304-3975(98)00272-2
fatcat:2ctscsnpxrg6zbu2cmcgo3raoi
*the*visual representations used are drawings*of*graphs and ordered sets. In this talk, we survey recent advances in*the*theory and practice*of*graph drawing. ...*The*visualization*of*conceptual structures is a key component*of*support tools for complex applications in science and engineering. ... This would provide graphical user interfaces with*the*flexibility*of*fitting drawings in arbitrarily*shaped*windows. ...##
###
Planar spanners and approximate shortest path queries among obstacles in the plane
[chapter]

1996
*
Lecture Notes in Computer Science
*

In this paper, we give a family

doi:10.1007/3-540-61680-2_79
fatcat:b74j7fgj6bbxtenmcxrzfqizeq
*of*algorithms for*the*above problem that achieve an interesting trade-off between*the**stretch*factor,*the*query time and*the*preprocessing bounds. ...*The*length*of*this path should be within a small constant factor c*of**the*length*of**the*shortest possible obstacle-avoiding s-t path measured in*the*Lv-metric. ... This subdivision is a*planar*graph where each face is a connected region called a cell.*The**shapes**of**the*cells have special significance, and are best described through*the*concept*of*boxes. ...##
###
A node-capacitated okamura-seymour theorem

2013
*
Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13
*

*The*classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face

*of*a

*planar*graph, there exists a feasible concurrent ... This answers an open question

*of*Chekuri and Kawarabayashi. More generally, we show that this holds in

*the*setting

*of*multi-commodity polymatroid networks introduced by Chekuri, et. al. ... Acknowledgements We are grateful to Chandra Chekuri and Bruce Shepherd for bringing

*the*node-capacitated problem to our attention and for their encouragement during

*the*course

*of*

*the*project. ...

##
###
A node-capacitated Okamura–Seymour theorem

2014
*
Mathematical programming
*

*The*classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face

*of*a

*planar*graph, there exists a feasible concurrent ... This answers an open question

*of*Chekuri and Kawarabayashi. More generally, we show that this holds in

*the*setting

*of*multi-commodity polymatroid networks introduced by Chekuri, et. al. ... Acknowledgements We are grateful to Chandra Chekuri and Bruce Shepherd for bringing

*the*node-capacitated problem to our attention and for their encouragement during

*the*course

*of*

*the*project. ...

##
###
SLICE: Enabling Greedy Routing in High Genus 3-D WSNs With General Topologies

2016
*
IEEE/ACM Transactions on Networking
*

, resulting in a lower routing

doi:10.1109/tnet.2015.2464312
fatcat:iwefmc4mtzezhke47qlwnxwbde
*stretch*. 2) This is*the*first work, to*the*best*of*our knowledge, that enables greedy routing in high genus 3-D WSNs with general topologies. ... Then, to achieve a lower distance distortion, we purposely propose a variation*of**the*Ricci flow algorithm, by which this open surface is flattened not to a*planar*annulus, but to a*planar*convex polygon ... Since*the*deformation process*of*Ricci flow is conformal (angle-preserving) [28] , [29] ,*the*value*of**the*distance*stretch*is closely related to*the**shape*changes from to :*the*more*shape*changes,*the*...##
###
Page 4567 of Mathematical Reviews Vol. , Issue 96h
[page]

1996
*
Mathematical Reviews
*

{For

*the*entire collection see MR 96g:05003.} 96h:05179 05C80 05C05 Maier, Robert S. (1-AZ; Tucson, AZ)*The**shape**of**stretched**planar**trees*. ... Summary: “We study*the*asymptotics*of*a ‘*stretched*’ model*of*un- labeled rooted*planar**trees*, in which*trees*are not taken equiprob- able but are weighted exponentially, according to their height. ...##
###
Rendering parametric surfaces in pen and ink

1996
*
Proceedings of the 23rd annual conference on Computer graphics and interactive techniques - SIGGRAPH '96
*

In particular, we introduce

doi:10.1145/237170.237287
dblp:conf/siggraph/WinkenbachS96
fatcat:eo64y737hff53ho5uezmthbkqu
*the*idea*of*"controlled-density hatching" for conveying tone, texture, and*shape*. ...*The*fine control over tone this method provides allows*the*use*of*traditional texture mapping techniques for specifying*the*tone*of*pen-and-ink illustrations. ... Acknowledgments We would like to thank Jorge Stolfi for many useful discussions during*the*early phase*of*this project. ...
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