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Page 7176 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
This extends, in a sense, Okamura’s theorem on edge-disjoint paths in planar graphs with two holes.”  ...  “Using (*), in Part II we give a criterion for the existence of edge- disjoint paths connecting certain vertices in a planar graph with three holes, provided that the so-called ‘parity condition’ holds  ... 

A combinatorial algorithm for the planar multiflow problem with demands located on three holes [article]

Maxim A. Babenko, Alexander V. Karzanov
2014 arXiv   pre-print
We consider an undirected multi(commodity)flow demand problem in which a supply graph is planar, each source-sink pair is located on one of three specified faces of the graph, and the capacities and demands  ...  It is known that such a problem has a solution if the cut and (2,3)-metric conditions hold, and that the solvability implies the existence of an integer solution.  ...  More precisely, a problem input consists of: a planar graph G = (V, E) with a fixed embedding in the plane; nonnegative integer capacities c(e) ∈ Z + of edges e ∈ E; a subset H ⊆ F G of faces, called holes  ... 
arXiv:1410.7208v1 fatcat:yh45qhrjdvfdrlwbujtoy4hxti

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

Chen Wang, Hongbo Jiang, Tianlong Yu, John C. S. Lui
2016 IEEE/ACM Transactions on Networking  
For a high genus 3-D surface network with holes, SLICE embeds it to a planar convex polygon with circular holes, where our proposed greedy routing variation can be applied.  ...  SLICE not only works for high genus 3-D surface WSNs, but also can be easily adapted to more general cases: high genus 3-D surface networks with holes, and high genus 3-D volume networks.  ...  TABLE I STORAGE I COST COMPARISON An intersection node is associated with more than one cuts or slice lines.  ... 
doi:10.1109/tnet.2015.2464312 fatcat:iwefmc4mtzezhke47qlwnxwbde

Near-Optimal Compression for the Planar Graph Metric [article]

Amir Abboud, Pawel Gawrychowski, Shay Mozes, Oren Weimann
2017 arXiv   pre-print
The Planar Graph Metric Compression Problem is to compactly encode the distances among k nodes in a planar graph of size n.  ...  This is an unexpected and decisive proof that weights can make planar graphs inherently more complex.  ...  Introduction The shortest path metric of planar graphs is one of the most popular and well-studied metrics in Computer Science.  ... 
arXiv:1703.04814v1 fatcat:s4yn7agdvvfytn7qugtwor646u

Near-Optimal Compression for the Planar Graph Metric [chapter]

Amir Abboud, Pawel Gawrychowski, Shay Mozes, Oren Weimann
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
The Planar Graph Metric Compression Problem is to compactly encode the distances among k nodes in a planar graph of size n.  ...  This is an unexpected and decisive proof that weights can make planar graphs inherently more complex.  ...  Introduction The shortest path metric of planar graphs is one of the most popular and well-studied metrics in Computer Science.  ... 
doi:10.1137/1.9781611975031.35 dblp:conf/soda/AbboudGMW18 fatcat:q25ljpjydvbrnhbd3igman3zq4

Metric Based Quadrilateral Mesh Generation [article]

Wei Chen, Xiaopeng Zheng, Jingyao Ke, Na Lei, Zhongxuan Luo and Xianfeng Gu
2018 arXiv   pre-print
Each quad-mesh induces a Riemannian metric satisfying special conditions: the metric is a flat metric with cone signualrites conformal to the original metric, the total curvature satisfies the Gauss-Bonnet  ...  Based on discrete Ricci flow and conformal structure deformation, one can obtain a metric satisfying all the conditions and obtain the desired quad-mesh.  ...  As shown in Fig. 2 , given a planar rectangle with two circular holes, a special flat metric is computed with a single singularity, whose index is −4.  ... 
arXiv:1811.12604v1 fatcat:hfps24fqfzhi5p3y5wqfytli34

An efficient algorithm for packing cuts and (2,3)-metrics in a planar graph with three holes [article]

Alexander V. Karzanov
2018 arXiv   pre-print
We consider a planar graph G in which the edges have nonnegative integer lengths such that the length of every cycle of G is even, and three faces are distinguished, called holes in G.  ...  It is known that there exists a packing of cuts and (2,3)-metrics with nonnegative integer weights in G which realizes the distances within each hole.  ...  metrics on V , then PMP has an integer solution, where a 4f -metric is generated by a mapping γ : V → V K with K being a planar graph with four faces [4] .  ... 
arXiv:1803.07020v1 fatcat:cc5uudmwtfeedkwi4lvzthcmsq

Resilient Routing for Sensor Networks Using Hyperbolic Embedding of Universal Covering Space

Wei Zeng, Rik Sarkar, Feng Luo, Xianfeng Gu, Jie Gao
2010 2010 Proceedings IEEE INFOCOM  
We study how to characterize the families of paths between any two nodes s, t in a sensor network with holes.  ...  Greedy routing to a particular image is guaranteed with success to find a path with a given homotopy type.  ...  This work is partially supported by NS-FCCF448399, ONRN00140910228, and NSFC60628202. J. Gao and R. Sarkar are partially supported by NSF CAREER Award CNS-0643687.  ... 
doi:10.1109/infcom.2010.5461988 dblp:conf/infocom/ZengSLGG10 fatcat:zynqmtc5vbcfvksyushlfpzgp4

Page 824 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
Secondly, we study the dilation of Yao @-graphs in the /\-metric. Finally, we study the size of a graph with no dilation in the /,-metric.”  ...  Summary: “The existing literature gives efficient algorithms for mapping trees or less restrictively outerplanar graphs on a given set of points in a plane, so that the edges are drawn planar and as straight  ... 

Scalable routing in 3D high genus sensor networks using graph embedding

Xiaokang Yu, Xiaotian Yin, Wei Han, Jie Gao, Xianfeng Gu
2012 2012 Proceedings IEEE INFOCOM  
We study scalable routing for a sensor network deployed in complicated 3D settings such as underground tunnels in gas system or water system.  ...  The adjacency of the pants components is extracted as a high level routing map and stored at every node. With the hyperbolic metric one can use greedy routing to navigate within and across pants.  ...  The authors would like to acknowledge support from NSF through grants CNS-0643587, CNS-1016829, and CNS-1116881.  ... 
doi:10.1109/infcom.2012.6195678 dblp:conf/infocom/YuYHGG12 fatcat:rbmmkwsyizdmjha7cdowmdgqjm

Inapproximability for metric embeddings into $\mathbb{R}^{d}$

Jiří Matoušek, Anastasios Sidiropoulos
2010 Transactions of the American Mathematical Society  
The exponent c/d has the correct order of magnitude, since every n-point metric space can be embedded in R d with distortion O(n 2/d log 3/2 n) and such an embedding can be constructed in polynomial time  ...  We consider the problem of computing the smallest possible distortion for embedding of a given n-point metric space into R d , where d is fixed (and small).  ...  Acknowledgment We thank Jussi Väisälä for providing us with a much better proof of Theorem 2.1(i) and (iii). We would like to thank Marianna Csörnyei for kindly answering a question of J.  ... 
doi:10.1090/s0002-9947-2010-05186-4 fatcat:wfptfpo3tzhsvff23drkaack4i

Scalable and Fully Distributed Localization in Large-Scale Sensor Networks

Miao Jin, Su Xia, Hongyi Wu, Xianfeng Gu
2017 Axioms  
A landmark node-based graph may have dangling vertices or edges as shown in Figure 2. A dangling vertex is a vertex belonging to more than one boundary.  ...  An edge connecting two neighboring vertices is the shortest path between the two landmarks in the network. A face of the planar graph is an n-polygon with n ≤ 3.  ... 
doi:10.3390/axioms6020015 fatcat:cd3qfl37kncajg6vskhocurrbe

ARROW: Azimuth-Range ROuting for large-scale Wireless sensor networks

Pawel Kulakowski, Esteban Egea-Lopez, Joan Garcia-Haro, Luis Orozco-Barbosa
2013 EURASIP Journal on Wireless Communications and Networking  
Moreover, ARROW is supplemented with a simple yet effective forwarder resolution protocol, also introduced in this study, allowing the fast and loop-free selection of the forwarding node in a hop-to-hop  ...  ARROW goes a step further on the design of geographic routing protocols by defining a simple and robust routing protocol whose operation principles completely free the network nodes of the burden of keeping  ...  It was supported by the Spanish MICINN, Consolider Programme, Plan E funds and CALM TEC2010-21405-C02-02, "Programa de Ayudas a Grupos de Exelencia de la Region de Murcia, Fundacion Seneca" programmes.  ... 
doi:10.1186/1687-1499-2013-93 fatcat:pokhmcdo4fcbpmbrgnhtxxpn74

Computational Conformal Geometry Behind Modern Technologies

Xianfeng Gu, Feng Luo, Shing-Tung Yau
2020 Notices of the American Mathematical Society  
The three curvatures correspond to the three cases (i), (ii) and (iii) above. The uniformization theorem also holds for compact surfaces with boundaries.  ...  : (i) the unit sphere 2 , (ii) a flat torus, or 2 , or 2 − {0} or (iii) a hyperbolic surface ℍ 2 /Γ, where Γ is a discrete torsion-free subgroup of isometries of the hyperbolic plane ℍ 2 .  ... 
doi:10.1090/noti2164 fatcat:io6e7wjhl5gfhkocwynrjbesuq

User-preference-based automated level generation for platform games

Nick Nygren, Jorg Denzinger, Ben Stephenson, John Aycock
2011 2011 IEEE Conference on Computational Intelligence and Games (CIG'11)  
In this paper, we present a level generation method that expands these standard kinds of levels by integrating puzzle based content that requires the player to explore the level in order to solve it.  ...  With these choices comes the need to elicit what kind of level a user would like to play at the current time, which is also covered by our level generation system.  ...  Graphs with longer path lengths will be more likely to be planar, and then easier to convert to a grid. This also prevents the start and finish of the level from being placed side by side.  ... 
doi:10.1109/cig.2011.6031989 dblp:conf/cig/NygrenDSA11 fatcat:oqzr5h45wrej5ldtys3hocwpdi
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