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A Note on the Practicality of Maximal Planar Subgraph Algorithms [article]

Markus Chimani, Karsten Klein, Tilo Wiedera
2016 arXiv   pre-print
Given a graph G, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of G with the maximum number of edges.  ...  We report on an exploratory study on the relative merits of the diverse approaches, focusing on practical runtime, solution quality, and implementation complexity.  ...  In the latter case, however, all known linear-time algorithms can be extended to extract a witness of non-planarity in the form of a Kuratowski subdivision in O(n) time.  ... 
arXiv:1608.07505v1 fatcat:mgexneb2qndlpjbnwquzlvnxfy

Minimum projective linearizations of trees in linear time [article]

Lluís Alemany-Puig, Juan Luis Esteban, Ramon Ferrer-i-Cancho
2021 arXiv   pre-print
Here we correct an error in HS's algorithm for the planar case, show its relationship with the projective case, and derive simple algorithms for the projective and planar cases that run without a doubt  ...  The Minimum Linear Arrangement problem (MLA) consists of finding a mapping π from vertices of a graph to distinct integers that minimizes ∑_{u,v}∈ E|π(u) - π(v)|.  ...  Iordanskii for helpful discussions. LAP is supported by Secretaria d'Universitats i Recerca de la Generalitat de Catalunya and the Social European Fund.  ... 
arXiv:2102.03277v4 fatcat:uotj5jiwbfbclguwc5odlriwqe

The minimum spanning tree problem on a planar graph

Tomomi Matsui
1995 Discrete Applied Mathematics  
This note presents a linear time algorithm for the minimum spanning tree problem on a planar graph. Cheriton and Tarjan [l] have proposed a linear time algorithm for this problem.  ...  The time complexity of our algorithm is the same as that of Cheriton and Tarjan's algorithm. Different from Cheriton and Tarjan's algorithm, our algorithm does not require the clean-up activity.  ...  Acknowledgement I am grateful to Takao Nishizeki for many useful suggestions.  ... 
doi:10.1016/0166-218x(94)00095-u fatcat:rbmyp6ga3jga5m2k5qqnxby4mi

Minimum projective linearizations of trees in linear time

Lluís Alemany-Puig, Juan Luis Esteban, Ramon Ferrer-i-Cancho
2021 Information Processing Letters  
Here we correct an error in HS's algorithm for the planar case, show its relationship with the projective case, and derive simple algorithms for the projective and planar cases that run without a doubt  ...  The Minimum Linear Arrangement problem (MLA) consists of finding a mapping π from vertices of a graph to distinct integers that minimizes {u,v}∈E |π (u) − π (v)|.  ...  Iordanskii for helpful discussions. We thank C. Gómez-Rodríguez for making us aware of reference [2] .  ... 
doi:10.1016/j.ipl.2021.106204 fatcat:htinfu24nnfrzjqm5kbxj2tafq

Information multicast in (pseudo-)planar networks: Efficient network coding over small finite fields

Tang Xiahou, Zongpeng Li, Chuan Wu
2013 2013 International Symposium on Network Coding (NetCod)  
on a common face, general planar networks, and apex networks.  ...  The following cases of (pseudo-)planar types of networks are studied: outer-planar networks where all nodes colocate on a common face, relay/terminal co-face networks where all relay/terminal nodes co-locate  ...  Code assignment algorithms are designed with linear time complexity over GF (3) and quadratic time complexity over GF (4) .  ... 
doi:10.1109/netcod.2013.6570828 dblp:conf/netcod/XiahouLW13 fatcat:xreadk2dtrcvhpaafxs5ripzqa

Refining the Analysis of Divide and Conquer: How and When [article]

Jeremy Barbay, Carlos Ochoa, Pablo Perez-Lantero
2015 arXiv   pre-print
Divide-and-conquer is a central paradigm for the design of algorithms, through which some fundamental computational problems, such as sorting arrays and computing convex hulls, are solved in optimal time  ...  A finer analysis of those problems yields complexities within O(n(1 + H(n_1, ..., n_k))) ⊆ O(n(1+k)) ⊆ O(nn) in the worst case over all instances of size n composed of k "easy" fragments of respective  ...  The time complexity T (n) of this algorithm follows the recurrence T (n) ≤ T ( n 2 ) + O(n), which yields a time complexity within O(n log n).  ... 
arXiv:1505.02820v3 fatcat:c6j6os6abjbxldb6o53iu6sxme

Clustered Level Planarity [chapter]

Michael Forster, Christian Bachmaier
2004 Lecture Notes in Computer Science  
For connected clustered level graphs we show that clustered k-level planarity can be tested in O(k|V |) time.  ...  Recently, several variations of planarity have been studied for advanced graph concepts such as k-level graphs [16], [15], [13], [14], [11], [12], [10], [6] and clustered graphs [7], [5] .  ...  Chandramouli and Diwan [3] present a linear time algorithm for triconnected DAGs. Leipert et al.  ... 
doi:10.1007/978-3-540-24618-3_18 fatcat:5si6ku52o5ef5jgcmpqn6fgcji

Page 4275 of Mathematical Reviews Vol. , Issue 83j [page]

1983 Mathematical Reviews  
testing and embedding’ [the authors, “The left-right algorithm for planarity testing and embedding in linear time”, to appear].  ...  Mach. 21 (1979), 549-568; MR 50 #11841] produced the first algorithm for testing planarity of graphs in linear time. Their proof of linearity relies on a lemma associated with the computing process.  ... 

A linear-processor algorithm for depth-first search in planar graphs

Gregory E. Shannon
1988 Information Processing Letters  
We present an n-processor and O(lo~n)-time parallel RAM algorithm for finding a depth-first-search tree in an n·vertex planar graph.  ...  The algorithm is based on a new n-processor algorithm for finding a cyclic separator in a planar graph and Smith's original parallel depth-first-search algorithm for planar graphs [Smi86].  ...  Acknowledgements I would like to thank Greg Frederickson and Susan Rodger for reviewing early drafts of this paper.  ... 
doi:10.1016/0020-0190(88)90048-8 fatcat:eluthznvlrhgfkcwi3mkynbpdy

Linear-time algorithm for vertex 2-coloring without monochromatic triangles on planar graphs [article]

Michał Karpiński, Krzysztof Piecuch
2021 arXiv   pre-print
In this paper we are positively answering the question posed in our previous work, namely, if there exists an algorithm solving 2-coloring without monochromatic triangles on planar graphs with linear-time  ...  complexity.  ...  For the positive result one can look for an algorithm that finds χ 3 (G) in graphs with ∆(G) ≥ 5 (where ∆(G) is the largest vertex degree of G).  ... 
arXiv:2110.04606v1 fatcat:3eqk7dsi7bahlc3xxlffj3z6cu

Linear-Time Algorithms for Hole-free Rectilinear Proportional Contact Graph Representations

M. Jawaherul Alam, Therese Biedl, Stefan Felsner, Andreas Gerasch, Michael Kaufmann, Stephen G. Kobourov
2013 Algorithmica  
For a planar 3-tree we give a linear-time algorithm for a hole-free proportional contact representation with 8-sided rectilinear polygons.  ...  We improve this result by giving a linear-time algorithm that produces a hole-free proportional contact representation of a maximal planar graph with a 10-sided rectilinear polygons.  ...  We also give a linear-time algorithm for a hole-free proportional contact representation of a planar 3-tree with 8-sided rectilinear polygons.  ... 
doi:10.1007/s00453-013-9764-5 fatcat:jgc76lhl2nfutdu6fwpm5x5c6i

Linear-Time Algorithms for Hole-Free Rectilinear Proportional Contact Graph Representations [chapter]

Muhammad Jawaherul Alam, Therese Biedl, Stefan Felsner, Andreas Gerasch, Michael Kaufmann, Stephen G. Kobourov
2011 Lecture Notes in Computer Science  
For a planar 3-tree we give a linear-time algorithm for a hole-free proportional contact representation with 8-sided rectilinear polygons.  ...  We improve this result by giving a linear-time algorithm that produces a hole-free proportional contact representation of a maximal planar graph with a 10-sided rectilinear polygons.  ...  We also give a linear-time algorithm for a hole-free proportional contact representation of a planar 3-tree with 8-sided rectilinear polygons.  ... 
doi:10.1007/978-3-642-25591-5_30 fatcat:5qnfgojplfc4pa7n2s2ocmal54

Fingerprinting/indoor positioning using complex planar splines

Irina Strelkovskaya, Irina Solovskaya, Juliya Strelkovska
2021 Journal of Electrical Engineering  
and linear complex planar splines is proposed. the construction of linear complex planar splines is considered, their coefficients are found. finding the error in determining the coordinates of the user's  ...  This concerns, first of all, methods for determining the local location of LPS users in premises, if there is a high concentration of users and the presence of difficulties in the propagation of radio  ...  Let us construct for the considered area shown in Fig. 2 and Fig. 3 linear complex planar spline (Fig. 4 ). P x y Fig. 4 .  ... 
doi:10.2478/jee-2021-0057 fatcat:a5gjbphzojg33i52vfjhzcb6va

Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs [chapter]

René van Bevern, Sepp Hartung, Frank Kammer, Rolf Niedermeier, Mathias Weller
2012 Lecture Notes in Computer Science  
We present a linear-time kernelization algorithm that transforms a given planar graph G with domination number γ(G) into a planar graph G of size O(γ(G)) with γ(G) = γ(G ).  ...  In terms of parameterized algorithmics, this implies a linear-size problem kernel for the NP-hard Dominating Set problem on planar graphs, where the kernelization takes linear time.  ...  On planar graphs, a linear-size problem kernel for Dominating Set is computable in linear time.  ... 
doi:10.1007/978-3-642-28050-4_16 fatcat:cvbceyuhu5crnjtfyrt5v7mstm

On approximating a vertex cover for planar graphs

R. Bar-Yehuda, S. Even
1982 Proceedings of the fourteenth annual ACM symposium on Theory of computing - STOC '82  
Two results are presented: (i) A linear time approximation algorithm for which the (error) performance bound is 2/3. (2) An 0(n log n) time approximation scheme. i.  ...  We say that e is a performance bound of A if for every graph IVCA(-IVC*I fvc*l Gavril suggested a linear-time approximation algorithm for which e = 1 (see [i] page 134).  ...  Michael Rodeh for his comment which led to the linear-time complexity analysis of the algorithm of Section 4.  ... 
doi:10.1145/800070.802205 dblp:conf/stoc/Bar-YehudaE82 fatcat:nklxnmrwsfdsvdzfxvzw6wvtpq
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