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A Linear-Time Algorithm to Find Independent Spanning Trees in Maximal Planar Graphs
[chapter]

2000
*
Lecture Notes in Computer Science
*

*In*this paper we give

*a*

*linear*-

*time*

*algorithm*

*to*

*find*k

*independent*

*spanning*

*trees*

*in*

*a*k-connected

*maximal*

*planar*

*graph*rooted at any designated vertex. ... Given

*a*

*graph*G,

*a*designated vertex r and

*a*natural number k, we wish

*to*

*find*k "

*independent*"

*spanning*

*trees*of G rooted at r, that is, k

*spanning*

*trees*such that, for any vertex v, the k paths connecting ...

*In*this paper we give

*a*simple

*linear*-

*time*

*algorithm*

*to*

*find*five

*independent*

*spanning*

*trees*of

*a*5-connected

*maximal*

*planar*

*graph*rooted at any designated vertex. ...

##
###
Page 3217 of Mathematical Reviews Vol. , Issue 98E
[page]

1998
*
Mathematical Reviews
*

Our

*algorithm*can also*find*depth-first*spanning**trees*of permutation*graphs**in**linear**time*, improving the recent*algorithm*on permutation*graphs*which takes O(n loglogn)*time*.” 98e:68200 68R10 05C35 Dijidjev ... Moreover, we give an*algorithm*of*independent*interest: computing*a*shortest path*tree*, or*finding**a*negative cycle*in*O(log’ n)*time*using O(n) work.” ...##
###
Fixed-parameter tractability results for full-degree spanning tree and its dual

2009
*
Networks
*

These problems are dual

doi:10.1002/net.20353
fatcat:3dufkge6abgxvjkpewufyipqg4
*to*each other:*In*Maximum Full-Degree*Spanning**Tree*, the task is*to**find**a**spanning**tree*for*a*given*graph*that*maximizes*the number of vertices that preserve their degree. ... Moreover, we present subexponential-*time**algorithms**in*the case of*planar**graphs*. ... Maximum Full-Degree*Spanning**Tree**in**Planar**Graphs*The reduction from*Independent*Set*to*Maximum Full-Degree*Spanning**Tree*(FDST) that is given*in*[3] already shows that FDST is W[1]-hard with respect ...##
###
Fixed-Parameter Tractability Results for Full-Degree Spanning Tree and Its Dual
[chapter]

2006
*
Lecture Notes in Computer Science
*

These problems are dual

doi:10.1007/11847250_19
fatcat:tvodrx6z5beb7kkwvuxipjl6fe
*to*each other:*In*Maximum Full-Degree*Spanning**Tree*, the task is*to**find**a**spanning**tree*for*a*given*graph*that*maximizes*the number of vertices that preserve their degree. ... Moreover, we present subexponential-*time**algorithms**in*the case of*planar**graphs*. ... Maximum Full-Degree*Spanning**Tree**in**Planar**Graphs*The reduction from*Independent*Set*to*Maximum Full-Degree*Spanning**Tree*(FDST) that is given*in*[3] already shows that FDST is W[1]-hard with respect ...##
###
Page 3715 of Mathematical Reviews Vol. , Issue 99f
[page]

1999
*
Mathematical Reviews
*

*maximal*

*independent*set

*in*

*a*

*linear*hypergraph. ... Summary: “We present

*a*randomized parallel

*algorithm*with polylogarithmic expected running

*time*for

*finding*

*a*

*maximal*

*in*- dependent set

*in*

*a*

*linear*hypergraph.” 99f:05111 05C85 05C70 68R10 Uno, Takeaki ...

##
###
Page 8816 of Mathematical Reviews Vol. , Issue 2002M
[page]

2002
*
Mathematical Reviews
*

Summary: “Given an undirected

*graph*with weights associated with its edges, the degree-constrained minimum*spanning**tree*problem consists*in**finding**a*minimum*spanning**tree*of the given*graph*, subject ...*Algorithms**to**find*all the elementary cycles, or*to*detect, if one exists,*a*negative cycle*in*such*a**graph*are well explored. ...##
###
Completely Independent Spanning Trees in Maximal Planar Graphs
[chapter]

2002
*
Lecture Notes in Computer Science
*

*In*this paper, we show that there are two completely

*independent*

*spanning*

*trees*

*in*any 4-connected

*maximal*

*planar*

*graph*. Our proof induces

*a*

*linear*-

*time*

*algorithm*for

*finding*such

*trees*. ... Let G be

*a*

*graph*. Let T1, T2, . . . , T k be

*spanning*

*trees*

*in*G. ... From our proof,

*a*

*linear*-

*time*

*algorithm*for

*finding*such

*trees*is obtained. ...

##
###
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. ... There are several heuristic, approximative, and exact*algorithms**to*tackle the problem, but---*to*the best of our knowledge---they have never been compared competitively*in*practice. ... The*algorithmically*simplest way*to**find**a**maximal**planar*subgraph is*to*start with the empty*graph*and*to*insert each edge (*in*random order) unless the*planarity*test fails. ...##
###
Enumeration of Enumeration Algorithms
[article]

2016
*
arXiv
*
pre-print

*In*this paper, we enumerate enumeration problems and

*algorithms*. This survey is under construction. If you know some results not

*in*this survey or there is anything wrong, please let me know. ... c(n) is the

*time*complexity

*to*

*find*an optimal solution

*to*

*a*problem with n (0, 1) variables. Reference [142] Enumeration of all paths

*in*

*a*

*graph*Input

*A*

*graph*G = (V, E). Output All paths

*in*G. ... Reference [64] 2.35.19 Enumeration of the k best

*spanning*

*trees*

*in*

*a*

*planar*

*graph*Input

*A*

*planar*

*graph*G = (V, E) and an integer k. Output The k best

*spanning*

*trees*of G. ...

##
###
Page 7194 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

These

*algorithms*lead*to**linear*-*time**algorithms*that determine whether*a*hierarchical*graph*is series-parallel or outer-*planar*and*to**linear*-space*algorithms*for generating*a*for- bidden subgraph of*a*... We also give*linear**time*sequential*algorithms*for minimally augmenting*a**spanning**tree*into*a*2-edge- connected or biconnected*graph*using edges from the original*graph*.” ...##
###
A 9k kernel for nonseparating independent set in planar graphs
[article]

2012
*
arXiv
*
pre-print

We prove that

arXiv:1207.4666v1
fatcat:axjyplfhszfovbba5z3kruvo5m
*graphs*that contain no separator consisting of only degree two vertices contain (*a*)*a**spanning**tree*with at least n/4 leaves and (b)*a*nonseparating*independent*set of size at least n/9 ( ... We also show*a*very simple 5k-vertices kernel for*Planar*Max Leaf, which results*in**a*lower bound of (5/4 - epsilon)k vertices for the kernel of*Planar*Connected Dominating Set (also under P \ne NP). ...*Finding**a**spanning**tree*with many leaves Kleitman and West [8] showed how*to**find**a**spanning**tree*with at least n/4 leaves*in**a**graph*of minimum degree 3. ...##
###
A nearly optimal parallel algorithm for constructing maximal independent set in planar graphs

1988
*
Theoretical Computer Science
*

The key subroutine of the

doi:10.1016/0304-3975(88)90106-5
fatcat:5kbfw6newnhb7hcv6hznlknxnu
*algorithm*is an O(log n)*time*, O(n) processor parallel*algorithm*for constructing*a**maximal**independent*set*in**a*one-page*planar**graph*. ... This paper presents an efficient parallel*algorithm*for constructing*maximal**independent*set*in**planar**graphs*. ... edge set of ven as*a*list*in*arbitrary order. is is the weakest representation of*a**Algorithm*for constructing*maximal**independent*set*in*pkziar*graphs*35*graph*. ...##
###
Planarizing Graphs - A Survey and Annotated Bibliography

2001
*
Journal of Graph Algorithms and Applications
*

Given

doi:10.7155/jgaa.00032
fatcat:zftlx3a5jnesxff5hjymjewp5u
*a*finite, undirected, simple*graph*G, we are concerned with operations on G that transform it into*a**planar**graph*. ... While there are many*algorithmic*results about*planarization*through edge deletion, the results about vertex splitting, thickness, and crossing number are mostly of*a*structural nature. ... with n − 1 edges (assume that G is connected), and that*a**spanning**tree*can be found*in**linear**time*. ...##
###
Page 2013 of Mathematical Reviews Vol. , Issue 96d
[page]

1996
*
Mathematical Reviews
*

Comput. 5 (1976), no. 4, 724-742; MR 56 #4783] have proposed

*a**linear**time**algorithm*for*finding**a**spanning**tree*of minimal weight on*a**planar**graph*. ... The*algorithm*deals with*a*pair of*a**planar**graph*and its dual gaph and breeds both*a*minimum*spanning**tree*of the original*graph*and*a*maximum*spanning**tree*of*a*dual*graph*. ...##
###
Combining Lagrangian Decomposition with an Evolutionary Algorithm for the Knapsack Constrained Maximum Spanning Tree Problem
[chapter]

2007
*
Lecture Notes in Computer Science
*

or with

doi:10.1007/978-3-540-71615-0_16
fatcat:k4m3oeeseferjavcw2h33yw2ki
*a*very small remaining gap*in*reasonable*time*. ... We present*a*Lagrangian decomposition approach for the Knapsack Constrained Maximum*Spanning**Tree*problem yielding upper bounds as well as heuristic solutions. ...*In*case of complete*graphs*, the knapsack capacity is c = 20·|V |−20,*in*case of (*maximal*)*planar**graphs*c = 35 · |V |. ...
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