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Testing Full Outer-2-planarity in Linear Time [chapter]

Seok-Hee Hong, Hiroshi Nagamochi
2016 Lecture Notes in Computer Science  
This paper considers the problem of testing 2-planarity of a graph, in particular,testing full outer-2planarity of a graph.  ...  Based on these properties, we present a linear-time algorithm for testing fully outer-2-planarity of a graph G, where G is triconnected, biconnected and oneconnected.  ...  There is a linear-time algorithm that tests whether a given graph is fully outer-2-planar, and produces a fully outer-2-planar embedding of the graph if it exists.  ... 
doi:10.1007/978-3-662-53174-7_29 fatcat:zoxr6flo2feflf4spugwo7gpym

Beyond Outerplanarity [chapter]

Steven Chaplick, Myroslav Kryven, Giuseppe Liotta, Andre Löffler, Alexander Wolff
2018 Lecture Notes in Computer Science  
Thus, since outer k-planar graphs have bounded treewidth, closed outer k-planarity is linear-time testable by Courcelle's Theorem.  ...  For each fixed k, these small balanced separators allow us to test outer k-planarity in quasi-polynomial time, i.e., none of these recognition problems are NP-hard unless ETH fails.  ...  Closed outer k-planarity and closed outer k-quasi-planarity can be expressed in MSO 2 . Thus, closed outer k-planarity can be tested in linear time.  ... 
doi:10.1007/978-3-319-73915-1_42 fatcat:r523bjfdojbotfnm7pxuzkmvry

Beyond Outerplanarity [article]

Steven Chaplick, Myroslav Kryven, Giuseppe Liotta, Andre Löffler, Alexander Wolff
2017 arXiv   pre-print
Thus, closed outer k-planarity is linear-time testable by Courcelle's Theorem.  ...  For fixed k, these small balanced separators allow us to obtain a simple quasi-polynomial time algorithm to test whether a given graph is outer k-planar, i.e., none of these recognition problems are NP-complete  ...  Closed outer k-planarity and closed outer k-quasi-planarity can be expressed in MSO 2 . Thus, closed outer k-planarity can be tested in linear time.  ... 
arXiv:1708.08723v2 fatcat:4bj7qcxbyfdspj4wxlinj3vs5q

Shrinking the Search Space for Clustered Planarity [chapter]

Markus Chimani, Karsten Klein
2013 Lecture Notes in Computer Science  
While it is long known that planarity-i.e., drawability without edge crossingsof graphs can be tested in polynomial (linear) time, the complexity for the clustered case is still unknown.  ...  Based thereon, we give new classes of polynomially testable graphs and a practically efficient exact planarity test for general clustered graphs based on an integer linear program.  ...  We can test clustered planarity of C in linear time. ILP and Experiments. We briefly recapitulate the ILP model of [2] , reduced to the special case of testing c-planarity.  ... 
doi:10.1007/978-3-642-36763-2_9 fatcat:prwhs7kambcnbd4hc4hrmk4bii

On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs

Michael A. Bekos, Sabine Cornelsen, Luca Grilli, Seok-Hee Hong, Michael Kaufmann
2016 Algorithmica  
In this paper, we present a polynomial-time algorithm to test whether a given graph is maximal outer-fan-planar.  ...  A graph is outer-fan-planar if it has a fan-planar embedding in which every vertex is on the outer face.  ...  It can be tested in linear time whether a graph is a complete 2-hop graph.  ... 
doi:10.1007/s00453-016-0200-5 fatcat:i357lisyqzgkdbt7a3cdy3uynm

On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs [chapter]

Michael A. Bekos, Sabine Cornelsen, Luca Grilli, Seok-Hee Hong, Michael Kaufmann
2014 Lecture Notes in Computer Science  
In this paper, we present a polynomial-time algorithm to test whether a given graph is maximal outer-fan-planar.  ...  Our main contribution is a polynomial time algorithm for the recognition of maximal outer-fan-planar graphs (Section 2).  ...  It can be tested in linear time whether a graph is a complete 2-hop graph.  ... 
doi:10.1007/978-3-662-45803-7_17 fatcat:55ue3f7zqjb73hs22hkvx6ifg4

On drawing a graph convexly in the plane (extended abstract) [chapter]

Hristo N. Djidjev
1995 Lecture Notes in Computer Science  
We obtain a necessary and sufficient condition for the existence and a linear Mgorithm for the construction of such an extension.  ...  Let G be a planar graph and H be a subgraph of G. Given any convex drawing of H, we investigate the problem of how to extend the drawing of H to a convex drawing of G.  ...  Using the information obtained during the planarity testing, one can find in linear time a planar representation of the graph, if it is planar.  ... 
doi:10.1007/3-540-58950-3_358 fatcat:6mem7zatwvcotmuexbu6rjfdum

Bax, but not Bcl-xL, decreases the lifetime of planar phospholipid bilayer membranes at subnanomolar concentrations

G. Basanez, A. Nechushtan, O. Drozhinin, A. Chanturiya, E. Choe, S. Tutt, K. A. Wood, Y.- T. Hsu, J. Zimmerberg, R. J. Youle
1999 Proceedings of the National Academy of Sciences of the United States of America  
We used planar phospholipid membranes to test the effect of full-length Bax and Bcl-x L synthesized in vitro and native Bax purified from bovine thymocytes.  ...  Release of proteins through the outer mitochondrial membrane can be a critical step in apoptosis, and the localization of apoptosis-regulating Bcl-2 family members there suggests they control this process  ...  USA 96 (1999) FIG. 2 . 2 Effect of full-length Bax and Bcl-xL on planar phospholipid bilayer membranes.  ... 
doi:10.1073/pnas.96.10.5492 pmid:10318911 pmcid:PMC21887 fatcat:jjqsq7xagrf43aousd2fr2qjbq

A Contactless Planar Inductive Sensor for Absolute Angular Displacement Measurement

Wenzheng Gao, Hong Shi, Qifu Tang
2021 IEEE Access  
A prototype with 63 and 64 period sense channels was designed and developed for experiments, and test results show that it was finally examined with short-period error of 14.7" and full range error of  ...  Copper pieces on the rotor PCB produce eddy current in the time-varying magnetic field and alter the outputs of two sense channels of pickup coils cyclically with the rotor's rotation.  ...  Full range error of outer sense channel in primary test FIGURE 9 .FIGURE 10 . 910 FIGURE 9.  ... 
doi:10.1109/access.2021.3131344 fatcat:v3vjzcnqfjft3knou435jg5pkm

Radial Level Planarity with Fixed Embedding

Guido Brückner, Ignaz Rutter
2021 Journal of Graph Algorithms and Applications  
We use these criteria to prove an "untangling" lemma that plays a key role in a simple level planarity test for the case where only the upward embedding is fixed.  ...  These notions allow for increasing degrees of freedom in their corresponding drawings. For the fixed level embedding there are known and easy to test level planarity criteria.  ...  Using Lemma 2 it can easily be tested in cubic time whether a (radial) level embedding is (radial) level planar. In Section 4, we improve this to linear time, see Lemma 4.  ... 
doi:10.7155/jgaa.00561 fatcat:zp7agvrrqba7neeh4wfuofqu6i

Radial Level Planarity Testing and Embedding in Linear Time

Christian Bachmaier, Franz J. Brandenburg, Michael Forster
2005 Journal of Graph Algorithms and Applications  
Our main results are linear time algorithms for radial level planarity testing and for computing a radial level planar embedding.  ...  Our algorithms extend level planarity testing and embedding algorithms, which use PQ-trees.  ...  Conclusion We have presented new linear time algorithms for testing radial level planarity and computing radial level planar embeddings.  ... 
doi:10.7155/jgaa.00100 fatcat:m4tzbflm45bc3pt6mwnqydtx6q

Radial Level Planarity Testing and Embedding in Linear Time [chapter]

Christian Bachmaier, Franz J. Brandenburg, Michael Forster
2004 Lecture Notes in Computer Science  
Our main results are linear time algorithms for radial level planarity testing and for computing a radial level planar embedding.  ...  Our algorithms extend level planarity testing and embedding algorithms, which use PQ-trees.  ...  Conclusion We have presented new linear time algorithms for testing radial level planarity and computing radial level planar embeddings.  ... 
doi:10.1007/978-3-540-24595-7_37 fatcat:7rm6x3xsdjeozojcxqalvkrooi

Silicon pixel-detector R&D for CLIC

A. Nürnberg
2016 Journal of Instrumentation  
with air-flow cooling in the inner vertex region) and pulsed power operation, complemented with ∼ 10 ns time stamping capabilities.  ...  Recent R&D achievements include results from beam tests with all types of hybrid assemblies.  ...  Acknowledgments The author would like to thank Jacobus Van Hoorne, Krzysztof Sielewicz and Walter Snoeys from the ALICE collaboration for providing the Investigator readout system and sharing the chips during the test  ... 
doi:10.1088/1748-0221/11/11/c11039 fatcat:mueevkmnxvfi3fl2vaxxznwcia

UNDISTORTED FROUDE MODEL FOR SURF ZONE SEDIMENT TRANSPORT

D.L. Kriebel, W.R. Dally, R.G. Dean
1986 Coastal Engineering Proceedings  
It appears that the initially planar profile unrealistically affects the breaker type and results in a more pronounced longshore bar and offshore slopes that are steeper than found in nature.  ...  Tests conducted to evaluate the criterion separating onshore-offshore transport suggested a higher value of the fall time parameter, H/wT, than was originally proposed by Dean (1973); this is interpreted  ...  The results corresponding to various elapsed times for the erosive case are shown in Prototype Results Refer to Saville's (1957) Large-Scale Wave Tank Tests. Initial Planar Profile of 1:15 Slope.  ... 
doi:10.9753/icce.v20.95 fatcat:fvpvas3hvrh75gay7quo7nxtjm

Finding Tutte Paths in Linear Time

Therese Biedl, Philipp Kindermann, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
This allows us to find some applications of Tutte paths (such as binary spanning trees and 2-walks) in linear time as well.  ...  In this paper, we give a new proof that 3-connected planar graphs have Tutte paths, which leads to a linear-time algorithm to find Tutte paths.  ...  With this, we can also find 2-walks and binary spanning trees in 3-connected planar graphs in linear time.  ... 
doi:10.4230/lipics.icalp.2019.23 dblp:conf/icalp/BiedlK19 fatcat:uugypmednbh3xefy7s444xdmj4
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