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

Sayaka Nagai, Shin-ichi Nakano
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.  ... 
doi:10.1007/3-540-40064-8_27 fatcat:zq634osxdrfxpkgijapv7amkye

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

Jiong Guo, Rolf Niedermeier, Sebastian Wernicke
2009 Networks  
These problems are dual 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  ... 
doi:10.1002/net.20353 fatcat:3dufkge6abgxvjkpewufyipqg4

Fixed-Parameter Tractability Results for Full-Degree Spanning Tree and Its Dual [chapter]

Jiong Guo, Rolf Niedermeier, Sebastian Wernicke
2006 Lecture Notes in Computer Science  
These problems are dual 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  ... 
doi:10.1007/11847250_19 fatcat:tvodrx6z5beb7kkwvuxipjl6fe

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]

Toru Hasunuma
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.  ... 
doi:10.1007/3-540-36379-3_21 fatcat:suimg4462zd6vgvilkhwwf3qai

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.  ...  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.  ... 
arXiv:1608.07505v1 fatcat:mgexneb2qndlpjbnwquzlvnxfy

Enumeration of Enumeration Algorithms [article]

Kunihiro Wasa
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.  ... 
arXiv:1605.05102v2 fatcat:bwmhesagkje5hmynqyij7jv224

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]

Lukasz Kowalik, Marcin Mucha
2012 arXiv   pre-print
We prove that 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.  ... 
arXiv:1207.4666v1 fatcat:axjyplfhszfovbba5z3kruvo5m

A nearly optimal parallel algorithm for constructing maximal independent set in planar graphs

Xin He
1988 Theoretical Computer Science  
The key subroutine of the 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.  ... 
doi:10.1016/0304-3975(88)90106-5 fatcat:5kbfw6newnhb7hcv6hznlknxnu

Planarizing Graphs - A Survey and Annotated Bibliography

Annegret Liebers
2001 Journal of Graph Algorithms and Applications  
Given 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.  ... 
doi:10.7155/jgaa.00032 fatcat:zftlx3a5jnesxff5hjymjewp5u

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]

Sandro Pirkwieser, Günther R. Raidl, Jakob Puchinger
2007 Lecture Notes in Computer Science  
or with 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 |.  ... 
doi:10.1007/978-3-540-71615-0_16 fatcat:k4m3oeeseferjavcw2h33yw2ki
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