A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Planar Embeddings of Graphs with Specified Edge Lengths

2007
*
Journal of Graph Algorithms and Applications
*

We consider the problem

doi:10.7155/jgaa.00145
fatcat:wo6t3akyq5czhnkgh5n3tspbqy
*of*finding a*planar**embedding**of*a (*planar*)*graph**with*a prescribed Euclidean*length*on every*edge*. ... This result is essentially tight: the problem becomes NP-hard if we consider instead*planar**embeddings**of**planar*3-connected infinitesimally rigid*graphs*, a natural relaxation*of*triangulations in this ... Our problem is then, given a*planar**graph**with*prescribed*lengths*on the*edges*, to construct a*planar**embedding**of*the*graph*that adheres to the*specified**edge**lengths*, and determine whether this*embedding*...##
###
Planar Embeddings of Graphs with Specified Edge Lengths
[chapter]

2004
*
Lecture Notes in Computer Science
*

We consider the problem

doi:10.1007/978-3-540-24595-7_26
fatcat:wt5y27jiwbhbfarpj2q3peeygi
*of*finding a*planar**embedding**of*a (*planar*)*graph**with*a prescribed Euclidean*length*on every*edge*. ... This result is essentially tight: the problem becomes NP-hard if we consider instead*planar**embeddings**of**planar*3-connected infinitesimally rigid*graphs*, a natural relaxation*of*triangulations in this ... Our problem is then, given a*planar**graph**with*prescribed*lengths*on the*edges*, to construct a*planar**embedding**of*the*graph*that adheres to the*specified**edge**lengths*, and determine whether this*embedding*...##
###
Flat Folding an Unassigned Single-Vertex Complex (Combinatorially Embedded Planar Graph with Specified Edge Lengths) without Flat Angles
[article]

2022
*
arXiv
*
pre-print

Equivalently, we efficiently characterize which combinatorially

arXiv:2204.03696v1
fatcat:vfk4mr4gfbe67gn3m35yhnznki
*embedded**planar**graphs**with*prescribed*edge**lengths*can fold flat, when all angles must be mountain or valley (not unfolded flat). ... Here we generalize these results to when the material forms a complex (instead*of*a manifold), and thus the angles are glued at the single vertex in the structure*of*an arbitrary*planar**graph*(instead ... This work grew out*of*an open problem session and a final project from the MIT class on Geometric Folding Algorithms: Linkages, Origami, Polyhedra (6.849) held Fall 2020. ...##
###
Flat Foldings of Plane Graphs with Prescribed Angles and Edge Lengths
[article]

2014
*
arXiv
*
pre-print

This characterization leads to a linear-time algorithm for testing flat foldability

arXiv:1408.6771v1
fatcat:5x3gvsiky5dbjly7rqei3heq24
*of*plane*graphs**with*prescribed*edge**lengths*and angles, and a polynomial-time algorithm for counting the number*of*distinct ... When can a plane*graph**with*prescribed*edge**lengths*and prescribed angles (from among {0,180^∘, 360^∘}) be folded flat to lie in an infinitesimally thin line, without crossings? ... Erik Demaine thanks Ilya Baran and Muriel Dulieu, and the authors*of*[2] , for many discussions attempting to solve this problem. ...##
###
Graph graphics: Theory and practice

1988
*
Computers and Mathematics with Applications
*

Most

doi:10.1016/0898-1221(88)90208-8
fatcat:b5gze7ag5jgptjg5tnnef7v3ja
*of*the problems described in this expository survey have constraints that relate to either minimizing the number*of*crossings or minimizing some function*of*the*edge**lengths*. ... Finally, several algorithms and heuristics for*graph*layout [some*with*applications to very large scale integration (VLSI)] will be discussed. ... Let G be a*graph**with*p nodes and q*edges*. A*graph*G can be*embedded*in a surface S if it can be drawn on S so that no pair*of**edges*cross. ...##
###
Flat foldings of plane graphs with prescribed angles and edge lengths

2015
*
Journal of Computational Geometry
*

This characterization leads to a linear-time algorithm for testing flat foldability

doi:10.20382/jocg.v9i1a3
dblp:journals/jocg/AbelDDELU18
fatcat:gf3flpgqljhfrpxa4n5hqqli4y
*of*plane*graphs**with*prescribed*edge**lengths*and angles, and a polynomial-time algorithm for counting the number*of*distinct ... When can a plane*graph**with*prescribed*edge**lengths*and prescribed angles (from among $\{0,180^\circ, 360^\circ\}$) be folded flat to lie in an infinitesimally thick line, without crossings? ... A preliminary version*of*these results were presented at the 22nd International Symposium on*Graph*Drawing [3] . ...##
###
Flat Foldings of Plane Graphs with Prescribed Angles and Edge Lengths
[chapter]

2014
*
Lecture Notes in Computer Science
*

This characterization leads to a linear-time algorithm for testing flat foldability

doi:10.1007/978-3-662-45803-7_23
fatcat:vndmmk7jyzb4ncdbgob3j4kmru
*of*plane*graphs**with*prescribed*edge**lengths*and angles, and a polynomial-time algorithm for counting the number*of*distinct ... When can a plane*graph**with*prescribed*edge**lengths*and prescribed angles (from among {0, 180 • , 360 • }) be folded flat to lie in an infinitesimally thin line, without crossings? ... A preliminary version*of*these results were presented at the 22nd International Symposium on*Graph*Drawing [3] . ...##
###
Minimum Length Embedding of Planar Graphs at Fixed Vertex Locations
[chapter]

2013
*
Lecture Notes in Computer Science
*

We consider the problem

doi:10.1007/978-3-319-03841-4_33
fatcat:gj6aw4zwybf2hjgix2jcctgohu
*of*finding a*planar**embedding**of*a*graph*at fixed vertex locations that minimizes the total*edge**length*. The problem is known to be NP-hard. ... We give polynomial time algorithms achieving an O( √ n log n) approximation for paths and matchings, and an O(n) approximation for general*graphs*. ... We learned about Sam Loyd's disjoint paths puzzle (which is not original to him) from Marcus Schaefer who has studied the history*of*such*planarity*puzzles. ...##
###
On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings
[article]

2017
*
arXiv
*
pre-print

For

arXiv:1708.09197v1
fatcat:ws6cfn2q4bhmne66dbcyxiisgu
*planar**graphs**of*higher degree, we present an algorithm that produces bi-monotone smooth orthogonal drawings*with*at most two segments per*edge*, which also guarantees a linear number*of**edges**with*... For*planar**graphs**of*max-degree 4, we analyze relationships between the*graph*classes that can be drawn bendless in the two models and we also prove NP-hardness for a restricted version*of*the bendless ... By*planarity*at least one copy*of**graph*B must be*embedded**with*the outerface*of*Fig. 5a . ...##
###
On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings
[chapter]

2018
*
Lecture Notes in Computer Science
*

For

doi:10.1007/978-3-319-73915-1_15
fatcat:kklzjrle5bcltipsyeokch23ru
*planar**graphs**of*higher degree, we present an algorithm that produces bi-monotone smooth orthogonal drawings*with*at most two segments per*edge*, which also guarantees a linear number*of**edges**with*... For*planar**graphs**of*max-degree 4, we analyze relationships between the*graph*classes that can be drawn bendless in the two models and we also prove NP-hardness for a restricted version*of*the bendless ... By*planarity*at least one copy*of**graph*B must be*embedded**with*the outerface*of*Fig. 5a . ...##
###
Graph Drawings with Relative Edge Length Specifications

2014
*
Canadian Conference on Computational Geometry
*

We study plane straight-line

dblp:conf/cccg/AichholzerHKR14
fatcat:wbpwlqpwara6hpfhcsjl36y7oq
*embeddings**of**graphs*where certain*edges*are*specified*to be longer than other*edges*. ... We analyze which*graphs*are universal in the sense that they allow a plane*embedding*for any total, strict order on the*edge**lengths*. ... Even if an*embedding**of*a*planar**graph*into the plane*with*certain*specified**edge**lengths*exists,*edge*crossings may be un-avoidable, for example, a K 4*with*four*edges**of*unit*length*and two non-adjacent ...##
###
Localization and routing in sensor networks by local angle information

2009
*
ACM transactions on sensor networks
*

*With*purely the connectivity information, determining whether a combinatorial

*graph*is a unit-disk

*graph*is NP-hard, and thus finding such an

*embedding*in the plane (

*with*neighboring nodes

*embedded*within ... This difficulty is also confirmed by the NP-hardness

*of*unit disk

*graph*

*embedding*. ... A

*planar*

*graph*is a

*graph*that can be

*embedded*in the plane

*with*no

*edge*crossings. ...

##
###
Localization and routing in sensor networks by local angle information

2005
*
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing - MobiHoc '05
*

*With*purely the connectivity information, determining whether a combinatorial

*graph*is a unit-disk

*graph*is NP-hard, and thus finding such an

*embedding*in the plane (

*with*neighboring nodes

*embedded*within ... This difficulty is also confirmed by the NP-hardness

*of*unit disk

*graph*

*embedding*. ... A

*planar*

*graph*is a

*graph*that can be

*embedded*in the plane

*with*no

*edge*crossings. ...

##
###
Folding Equilateral Plane Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

Equivalently, we show strong NP-completeness

doi:10.1007/978-3-642-25591-5_59
fatcat:dgii5ouolnbohcdgg2eo2fgkha
*of*deciding whether an abstract metric polyhedral complex*with*one central vertex has a noncrossing flat folded state*with*a*specified*"outside region". ... We consider two types*of*folding applied to equilateral plane*graph*linkages. ... We thank Ilya Baran for early discussions about instantaneous*graph*folding, in particular conjecturing Theorem 2. We also thank Muriel Dulieu for helpful discussions on this topic. ...##
###
FOLDING EQUILATERAL PLANE GRAPHS

2013
*
International journal of computational geometry and applications
*

Equivalently, we show strong NP-completeness

doi:10.1142/s0218195913600017
fatcat:ll4yb6jsgzcjfph4dq75icwysq
*of*deciding whether an abstract metric polyhedral complex*with*one central vertex has a noncrossing flat folded state*with*a*specified*"outside region". ... We consider two types*of*folding applied to equilateral plane*graph*linkages. ... We thank Ilya Baran for early discussions about instantaneous*graph*folding, in particular conjecturing Theorem 2. We also thank Muriel Dulieu for helpful discussions on this topic. ...
« Previous

*Showing results 1 — 15 out of 16,188 results*