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Algorithms for routing in planar graphs

M. Becker, K. Mehlhorn
1986 Acta Informatica  
We present algorithms for solving routing problems for twoterminal nets in planar graphs.  ...  Our algorithms run in time 2 O(n ) Cor general planar graphs and in time 0 (bnl for grid graph s wheTe n 1S the number of vert ices and b is the number of vertices on the boundary of the infinite face  ...  C In th is paper we will present algorithms for solving routing problems in planar graph s . We use the following notation . Definition: Let P = (V,E,Ne) be a planar routing problem, n = IV I .  ... 
doi:10.1007/bf00289496 fatcat:e7kaypzoxrglnpkhxyvqt3sene

A Geo-Routing Algorithm in Planar Graph for Ad Hoc Wireless Networks

Rashid Bin Muhammad
2007 21st International Conference on Advanced Information Networking and Applications Workshops (AINAW'07)  
The main contribution of this work is a fully distributed algorithm to extract the connected, planar graph for routing in the wireless networks.  ...  This paper presented a fully distributed algorithm to compute a planar subgraph for geo-routing in ad hoc wireless networks.  ...  And each proposal is replied by at Routing In this section we describe an algorithm for routing in planar graph obtained in the previous section.  ... 
doi:10.1109/ainaw.2007.23 dblp:conf/aina/Muhammad07 fatcat:jcofbios5balfg2ne4bwbugf2e

Void traversal for efficient non-planar geometric routing

Thomas Clouser, Adnan Vora, Timothy Fox, Mikhail Nesterenko
2013 Ad hoc networks  
Such algorithms require a planar graph to guarantee message delivery. The routing techniques for such guarantee usually center around the traversal of planar faces of the graph.  ...  In this paper we propose a non-planar void traversal technique that allows geometric routing algorithms to operate on non-planar graphs directly.  ...  Acknowledgments We would like to thank Ivan Stojmenovic of the University of Ottawa for his helpful comments.  ... 
doi:10.1016/j.adhoc.2013.05.013 fatcat:vmwdewtksjbexk2ryypjkiw2sa

A localized planarization algorithm for realistic wireless networks

Emi Mathews, Hannes Frey
2011 2011 IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks  
Planar graph routing works provably correct if the underlying network graph is connected and planar.  ...  In this work we exploit this locality property to build a new localized planarization algorithm, which is location fault tolerant and which produces planar connected graphs in most cases in realistic wireless  ...  Geographic routing algorithms such as GPSR and GOAFR could be applied at a macroscopic level, using the planar overlay graph provided by our planarization algorithm.  ... 
doi:10.1109/wowmom.2011.5986487 dblp:conf/wowmom/MathewsF11 fatcat:2vg56uwdfbei7kstezbplrnuxm

Book announcement

1992 Discrete Applied Mathematics  
An algorithmic framework for line searching. The track graph (Construction of the track graph). Summary). Steiner tree heuristics in sequential routing (Steiner tree heuristics for maze running.  ...  Genera1 planar routing). Nonplanar channel routing. Detailed routing in the knock-knee mode1 (Channel routing in the knock-knee model. Other detailed-routing graphs (The genera1 method.  ... 
doi:10.1016/0166-218x(92)90299-p fatcat:kkkpojidyvgifm6vpfwb5c2epi

A Distributed Geometric Routing Algorithm for Ad HocWireless Networks

Rashid Bin Muhammad
2007 Fourth International Conference on Information Technology (ITNG'07)  
The main contribution of this work is a fully distributed algorithm to extract the connected, planar graph for routing in the wireless networks.  ...  In this paper, we presented a fully distributed algorithm to compute a planar subgraph of the underlying wireless connectivity graph.  ...  Routing In this section we describe an algorithm for routing in planar graph obtained in the previous section. The algorithm is based on [5] and the basic idea is as follows.  ... 
doi:10.1109/itng.2007.4 dblp:conf/itng/Muhammad07 fatcat:qixnr7a6rffmbasjkknopg3d2q

WSN13-6: Routing on Overlay Graphs in Mobile Ad Hoc Networks

Sumesh J. Philip, Joy Ghosh, Hung Q. Ngo, Chunming Qiao
2006 IEEE Global Communications Conference, Exhibition, & Industry Forum (GLOBECOM)  
Recently, there has been considerable attention on face routing in planar graphs constructed from overlay graphs in wireless networks.  ...  We consider the problem of constructing a connected planar graph from the overlay graph, and geometric routing in such graphs.  ...  A DISTRIBUTED ALGORITHM FOR OVERLAY PLANAR GRAPH CONSTRUCTION We now describe a distributed algorithm that constructs a planar subgraph from the overlay graph by adding virtual edges and by removing redundant  ... 
doi:10.1109/glocom.2006.969 dblp:conf/globecom/PhilipGNQ06 fatcat:3obkf4ocufejdbxqg6cae73ile

Planar graph routing on geographical clusters

Hannes Frey, Daniel Görgen
2005 Ad hoc networks  
algorithm competes with existing solutions and even outperforms planar graph routing methods based on one-hop neighbor information.  ...  This paper finally gives an outline of further research directions which show that geographical clusters may be the key to solve some problems that come along with planar graph routing in wireless networks  ...  The face routing algorithm proposed there is an improvement of the planar graph routing algorithm introduced in [11] .  ... 
doi:10.1016/j.adhoc.2004.08.013 fatcat:rh54vg7bibffhfhs3wd4e326hi

Scalable geographic routing algorithms for wireless ad hoc networks

H. Frey
2004 IEEE Network  
This article provides a tutorial for this class of geographic routing algorithms and will discuss recent improvements to both greedy forwarding and routing in planar graphs.  ...  In recent years planar graph traversal has been investigated as one possible strategy to recover from such greedy routing failures.  ...  Additionally, improvements to planar graph routing are presented in this section. The characteristics of greedy and combined greedy and planar graph routing algorithms are outlined in section IV.  ... 
doi:10.1109/mnet.2004.1316756 fatcat:szjniplj4jhdpo4s4k3r54w354

Success guaranteed routing in almost Delaunay planar nets for wireless sensor communication

Md. Bahlul Haider, Shinji Imahori, Kokichi Sugihara
2011 International Journal of Sensor Networks (IJSNet)  
We show that the proposed routing strategy exhibits good performance if the underlying graph in the sensor network is the almost Delaunay planar net.  ...  We statistically analyze the efficiency of existing routing strategies in the almost Delaunay planar net.  ...  Acknowledgment This work is partly supported by a Grant-in-Aid for Scientific Research (B) (No. 20360044) of the Japanese Society for the Promotion of Science.  ... 
doi:10.1504/ijsnet.2011.038760 fatcat:s3s2xkjlpjgpzhvmckdvxn4fqy

Modeling and analyzing the correctness of geographic face routing under realistic conditions

Karim Seada, Ahmed Helmy, Ramesh Govindan
2007 Ad hoc networks  
radio irregularity, cause failure in planarization and consequently face routing.  ...  Finally, we conclude that in order to avoid all failures under arbitrary connectivity, we need a non-local algorithm that can search or propagate information for an unlimited number of hops.  ...  We would like to thank the anonymous reviewers for their feedback.  ... 
doi:10.1016/j.adhoc.2007.02.008 fatcat:fcd4656z6fdjdhqvkf35jkchvu

On a Conjecture Related to Geometric Routing [chapter]

Christos H. Papadimitriou, David Ratajczak
2004 Lecture Notes in Computer Science  
We also present a simple but provably robust version of greedy routing that works for any graph with a 3-connected planar spanning subgraph.  ...  We conjecture that any planar 3-connected graph can be embedded in the plane in such a way that for any nodes s and t, there is a path from s to t such that the Euclidean distance to t decreases monotonically  ...  We also thank the anonymous reviewers for their helpful comments.  ... 
doi:10.1007/978-3-540-27820-7_3 fatcat:jgle7mcclfdl7f6ishi4mb5bni

On a conjecture related to geometric routing

Christos H. Papadimitriou, David Ratajczak
2005 Theoretical Computer Science  
We also present a simple but provably robust version of greedy routing that works for any graph with a 3-connected planar spanning subgraph.  ...  We conjecture that any planar 3-connected graph can be embedded in the plane in such a way that for any nodes s and t, there is a path from s to t such that the Euclidean distance to t decreases monotonically  ...  We also thank the anonymous reviewers for their helpful comments.  ... 
doi:10.1016/j.tcs.2005.06.022 fatcat:7ihk3jbhlnhaddyernomqhph3i

Geographical Cluster-Based Routing in Sensing-Covered Networks

H. Frey, D. Gorgen
2006 IEEE Transactions on Parallel and Distributed Systems  
A recently proposed variant performs message forwarding along edges of a virtual overlay graph instead of using wireless links for planar graph construction directly.  ...  In this work we will proof a theoretical bound which is a sufficient condition for guaranteed delivery of this routing strategy applied in sensing covered networks.  ...  Similar to planar graph routing based on physical network links, not all edges of the aggregated unit disk graph may be utilized by the planar graph traversal method of the GCR algorithm since the network  ... 
doi:10.1109/tpds.2006.124 fatcat:m5lue2iqu5bprakiidxtrgbhni

Fast Geometric Routing with Concurrent Face Traversal [chapter]

Thomas Clouser, Mark Miyashita, Mikhail Nesterenko
2008 Lecture Notes in Computer Science  
CFR maintains its advantage over the other algorithms in pure form as well as in combination with greedy routing; on planar as well as on non-planar graphs.  ...  Our simulation results demonstrate that, on average, CFR significantly outperforms the best known geometric routing algorithms in the path stretch: the speed of message delivery.  ...  In Sect. 4, we discuss how the algorithm can be adapted for greedy routing and for use in non-planar graphs.  ... 
doi:10.1007/978-3-540-92221-6_23 fatcat:y5xge76dszg4pow4tsns24vrs4
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