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

2016
*
arXiv
*
pre-print

Given

arXiv:1608.07505v1
fatcat:mgexneb2qndlpjbnwquzlvnxfy
*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*. ...##
###
Minimum projective linearizations of trees in linear time
[article]

2021
*
arXiv
*
pre-print

Here we correct an error in HS's

arXiv:2102.03277v4
fatcat:uotj5jiwbfbclguwc5odlriwqe
*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. ...##
###
The minimum spanning tree problem on a planar graph

1995
*
Discrete Applied Mathematics
*

This note presents

doi:10.1016/0166-218x(94)00095-u
fatcat:rbmyp6ga3jga5m2k5qqnxby4mi
*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. ...##
###
Minimum projective linearizations of trees in linear time

2021
*
Information Processing Letters
*

Here we correct an error in HS's

doi:10.1016/j.ipl.2021.106204
fatcat:htinfu24nnfrzjqm5kbxj2tafq
*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*] . ...##
###
Information multicast in (pseudo-)planar networks: Efficient network coding over small finite fields

2013
*
2013 International Symposium on Network Coding (NetCod)
*

on

doi:10.1109/netcod.2013.6570828
dblp:conf/netcod/XiahouLW13
fatcat:xreadk2dtrcvhpaafxs5ripzqa
*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) . ...##
###
Refining the Analysis of Divide and Conquer: How and When
[article]

2015
*
arXiv
*
pre-print

Divide-and-conquer is

arXiv:1505.02820v3
fatcat:c6j6os6abjbxldb6o53iu6sxme
*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). ...##
###
Clustered Level Planarity
[chapter]

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. ...

##
###
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

1988
*
Information Processing Letters
*

We present an n-processor and O(lo~n)-

doi:10.1016/0020-0190(88)90048-8
fatcat:eluthznvlrhgfkcwi3mkynbpdy
*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. ...##
###
Linear-time algorithm for vertex 2-coloring without monochromatic triangles on planar graphs
[article]

2021
*
arXiv
*
pre-print

In this paper we are positively answering the question posed in our previous work, namely, if there exists an

arXiv:2110.04606v1
fatcat:3eqk7dsi7bahlc3xxlffj3z6cu
*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). ...##
###
Linear-Time Algorithms for Hole-free Rectilinear Proportional Contact Graph Representations

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. ...

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

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. ...

##
###
Fingerprinting/indoor positioning using complex planar splines

2021
*
Journal of Electrical Engineering
*

and

doi:10.2478/jee-2021-0057
fatcat:a5gjbphzojg33i52vfjhzcb6va
*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 . ...##
###
Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs
[chapter]

2012
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/978-3-642-28050-4_16
fatcat:cvbceyuhu5crnjtfyrt5v7mstm
*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*. ...##
###
On approximating a vertex cover for planar graphs

1982
*
Proceedings of the fourteenth annual ACM symposium on Theory of computing - STOC '82
*

Two results are presented: (i)

doi:10.1145/800070.802205
dblp:conf/stoc/Bar-YehudaE82
fatcat:nklxnmrwsfdsvdzfxvzw6wvtpq
*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. ...
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