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

2014
*
arXiv
*
pre-print

We consider an undirected multi(commodity)flow demand problem

arXiv:1410.7208v1
fatcat:yh45qhrjdvfdrlwbujtoy4hxti
*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*...##
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SLICE: Enabling Greedy Routing in High Genus 3-D WSNs With General Topologies

2016
*
IEEE/ACM Transactions on Networking
*

For

doi:10.1109/tnet.2015.2464312
fatcat:iwefmc4mtzezhke47qlwnxwbde
*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. ...##
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Near-Optimal Compression for the Planar Graph Metric
[article]

2017
*
arXiv
*
pre-print

The

arXiv:1703.04814v1
fatcat:s4yn7agdvvfytn7qugtwor646u
*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. ...##
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Near-Optimal Compression for the Planar Graph Metric
[chapter]

2018
*
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
*

The

doi:10.1137/1.9781611975031.35
dblp:conf/soda/AbboudGMW18
fatcat:q25ljpjydvbrnhbd3igman3zq4
*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. ...##
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Metric Based Quadrilateral Mesh Generation
[article]

2018
*
arXiv
*
pre-print

Each quad-mesh induces

arXiv:1811.12604v1
fatcat:hfps24fqfzhi5p3y5wqfytli34
*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. ...##
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An efficient algorithm for packing cuts and (2,3)-metrics in a planar graph with three holes
[article]

2018
*
arXiv
*
pre-print

We consider

arXiv:1803.07020v1
fatcat:cc5uudmwtfeedkwi4lvzthcmsq
*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] . ...##
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Resilient Routing for Sensor Networks Using Hyperbolic Embedding of Universal Covering Space

2010
*
2010 Proceedings IEEE INFOCOM
*

We study how to characterize the families of

doi:10.1109/infcom.2010.5461988
dblp:conf/infocom/ZengSLGG10
fatcat:zynqmtc5vbcfvksyushlfpzgp4
*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. ...##
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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 ...##
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Scalable routing in 3D high genus sensor networks using graph embedding

2012
*
2012 Proceedings IEEE INFOCOM
*

We study scalable routing for

doi:10.1109/infcom.2012.6195678
dblp:conf/infocom/YuYHGG12
fatcat:rbmmkwsyizdmjha7cdowmdgqjm
*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. ...##
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Inapproximability for metric embeddings into $\mathbb{R}^{d}$

2010
*
Transactions of the American Mathematical Society
*

The exponent c/d has the correct order of magnitude, since every n-point

doi:10.1090/s0002-9947-2010-05186-4
fatcat:wfptfpo3tzhsvff23drkaack4i
*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. ...##
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Scalable and Fully Distributed Localization in Large-Scale Sensor Networks

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. ...

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

2013
*
EURASIP Journal on Wireless Communications and Networking
*

Moreover, ARROW is supplemented

doi:10.1186/1687-1499-2013-93
fatcat:pokhmcdo4fcbpmbrgnhtxxpn74
*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. ...##
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Computational Conformal Geometry Behind Modern Technologies

2020
*
Notices of the American Mathematical Society
*

The

doi:10.1090/noti2164
fatcat:io6e7wjhl5gfhkocwynrjbesuq
*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 . ...##
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User-preference-based automated level generation for platform games

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. ...

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