Filters








16,188 Hits in 6.3 sec

Planar Embeddings of Graphs with Specified Edge Lengths

Sergio Cabello, Erik D. Demaine, Günter Rote
2007 Journal of Graph Algorithms and Applications  
We consider the problem 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  ... 
doi:10.7155/jgaa.00145 fatcat:wo6t3akyq5czhnkgh5n3tspbqy

Planar Embeddings of Graphs with Specified Edge Lengths [chapter]

Sergio Cabello, Erik D. Demaine, Günter Rote
2004 Lecture Notes in Computer Science  
We consider the problem 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  ... 
doi:10.1007/978-3-540-24595-7_26 fatcat:wt5y27jiwbhbfarpj2q3peeygi

Flat Folding an Unassigned Single-Vertex Complex (Combinatorially Embedded Planar Graph with Specified Edge Lengths) without Flat Angles [article]

Lily Chung, Erik D. Demaine, Dylan Hendrickson, Victor Luo
2022 arXiv   pre-print
Equivalently, we efficiently characterize which combinatorially 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.  ... 
arXiv:2204.03696v1 fatcat:vfk4mr4gfbe67gn3m35yhnznki

Flat Foldings of Plane Graphs with Prescribed Angles and Edge Lengths [article]

Zachary Abel, Erik D. Demaine, Martin L. Demaine, David Eppstein, Anna Lubiw, Ryuhei Uehara
2014 arXiv   pre-print
This characterization leads to a linear-time algorithm for testing flat foldability 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.  ... 
arXiv:1408.6771v1 fatcat:5x3gvsiky5dbjly7rqei3heq24

Graph graphics: Theory and practice

C. Esposito
1988 Computers and Mathematics with Applications  
Most 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.  ... 
doi:10.1016/0898-1221(88)90208-8 fatcat:b5gze7ag5jgptjg5tnnef7v3ja

Flat foldings of plane graphs with prescribed angles and edge lengths

Zachary Abel, Erik D. Demaine, Martin L. Demaine, David Eppstein, Anna Lubiw, Ryuhei Uehara
2015 Journal of Computational Geometry  
This characterization leads to a linear-time algorithm for testing flat foldability 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] .  ... 
doi:10.20382/jocg.v9i1a3 dblp:journals/jocg/AbelDDELU18 fatcat:gf3flpgqljhfrpxa4n5hqqli4y

Flat Foldings of Plane Graphs with Prescribed Angles and Edge Lengths [chapter]

Zachary Abel, Erik D. Demaine, Martin L. Demaine, David Eppstein, Anna Lubiw, Ryuhei Uehara
2014 Lecture Notes in Computer Science  
This characterization leads to a linear-time algorithm for testing flat foldability 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] .  ... 
doi:10.1007/978-3-662-45803-7_23 fatcat:vndmmk7jyzb4ncdbgob3j4kmru

Minimum Length Embedding of Planar Graphs at Fixed Vertex Locations [chapter]

Timothy M. Chan, Hella-Franziska Hoffmann, Stephen Kiazyk, Anna Lubiw
2013 Lecture Notes in Computer Science  
We consider the problem 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.  ... 
doi:10.1007/978-3-319-03841-4_33 fatcat:gj6aw4zwybf2hjgix2jcctgohu

On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings [article]

Michael A. Bekos, Henry Förster, Michael Kaufmann
2017 arXiv   pre-print
For 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 .  ... 
arXiv:1708.09197v1 fatcat:ws6cfn2q4bhmne66dbcyxiisgu

On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings [chapter]

Michael A. Bekos, Henry Förster, Michael Kaufmann
2018 Lecture Notes in Computer Science  
For 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 .  ... 
doi:10.1007/978-3-319-73915-1_15 fatcat:kklzjrle5bcltipsyeokch23ru

Graph Drawings with Relative Edge Length Specifications

Oswin Aichholzer, Michael Hoffmann, Marc J. van Kreveld, Günter Rote
2014 Canadian Conference on Computational Geometry  
We study plane straight-line 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  ... 
dblp:conf/cccg/AichholzerHKR14 fatcat:wbpwlqpwara6hpfhcsjl36y7oq

Localization and routing in sensor networks by local angle information

Jehoshua Bruck, Jie Gao, Anxiao (Andrew) Jiang
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.  ... 
doi:10.1145/1464420.1464427 fatcat:t2ywlq64ijchzokvmlmdkyuicy

Localization and routing in sensor networks by local angle information

Jehoshua Bruck, Jie Gao, Anxiao (Andrew) Jiang
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.  ... 
doi:10.1145/1062689.1062713 dblp:conf/mobihoc/BruckGJ05 fatcat:wfbjdixx25bzzfjwp4ik6goxbi

Folding Equilateral Plane Graphs [chapter]

Zachary Abel, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Jayson Lynch, Tao B. Schardl, Isaac Shapiro-Ellowitz
2011 Lecture Notes in Computer Science  
Equivalently, we show strong NP-completeness 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.  ... 
doi:10.1007/978-3-642-25591-5_59 fatcat:dgii5ouolnbohcdgg2eo2fgkha

FOLDING EQUILATERAL PLANE GRAPHS

ZACHARY ABEL, ERIK D. DEMAINE, MARTIN L. DEMAINE, SARAH EISENSTAT, JAYSON LYNCH, TAO B. SCHARDL, ISAAC SHAPIRO-ELLOWITZ
2013 International journal of computational geometry and applications  
Equivalently, we show strong NP-completeness 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.  ... 
doi:10.1142/s0218195913600017 fatcat:ll4yb6jsgzcjfph4dq75icwysq
« Previous Showing results 1 — 15 out of 16,188 results