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Algorithms for Maximum Internal Spanning Tree Problem for Some Graph Classes
[article]

2021
*
arXiv
*
pre-print

*For*a given

*graph*G, a

*maximum*

*internal*

*spanning*

*tree*of G is a

*spanning*

*tree*of G with

*maximum*number of

*internal*vertices. ... The

*Maximum*

*Internal*

*Spanning*

*Tree*(MIST)

*problem*is to find a

*maximum*

*internal*

*spanning*

*tree*of the given

*graph*. The MIST

*problem*is a generalization of the Hamiltonian path

*problem*. ...

*Algorithms*

*for*

*Maximum*

*Internal*

*Spanning*

*Tree*

*Problem*

*for*

*Some*

*Graph*

*Classes** ...

##
###
Grafalgo - A Library of Graph Algorithms and Supporting Data Structures (revised)
[article]

2016
*
arXiv
*
pre-print

This report provides an (updated) overview of Grafalgo, an open-source library of

arXiv:1601.01597v1
fatcat:tnnsmnbupje3fjte2efi2zmls4
*graph**algorithms*and the data structures used to implement them. ... The programs in this library were originally written to support a graduate*class*in advanced data structures and*algorithms*at Washington University. ... Minimum*Spanning**Tree**Problem*The objective of the minimum*spanning**tree**problem*is to find a*spanning**tree*of an edge-weighted*graph*that has the smallest total weight. ...##
###
Approximating node-weighted multicast trees in wireless ad-hoc networks

2009
*
Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing Connecting the World Wirelessly - IWCMC '09
*

*For*

*graph*

*classes*that admit

*spanning*

*trees*of

*maximum*degree at most d, we obtain a 0.775d-approximation

*algorithm*. ... We show that this result implies a 3.875-approximation

*algorithm*

*for*unit disk

*graphs*, an O(1/α 2 )-approximation

*algorithm*

*for*α-unit disk

*graphs*, and an O(λ)-approximation

*algorithm*

*for*(λ + 1)claw-free ... In this paper, we present a 0.775d-approximation

*algorithm*

*for*the

*problem*of computing a Steiner

*tree*with minimum total weight of the Steiner nodes

*for*

*graph*

*classes*that admit

*spanning*

*trees*of

*maximum*...

##
###
Page 67 of Mathematical Reviews Vol. , Issue 2003A
[page]

2003
*
Mathematical Reviews
*

A recent

*algorithm**for*the*maximum*clique*problem*is here used as a basis*for*developing an*algorithm**for*the weighted case. ... derive upper and lower bounds*for*the expected cost of the optimal*spanning**tree*. ...##
###
Minimum Connected Dominating Set for Certain Circulant Networks

2015
*
Procedia Computer Science
*

In general, the

doi:10.1016/j.procs.2015.07.401
fatcat:w2bu3v66cja23oullt52k7xt7y
*problem*is proved to be NP-hard. In this paper we find a Minimum Connected Dominating Set*for*certain Circulant Networks. ... The*Maximum*Leaf*Spanning**Tree*(MLST)*problem*is to find a*spanning**tree*of a*graph*with as many leaves as possible. ... Given a*graph*G, the*Maximum*Leaf*Spanning**Tree**problem*is to find the*maximum*number of vertices of degree one in a*spanning**tree*over all*spanning**trees*of G. Corresponding author. ...##
###
Page 3697 of Mathematical Reviews Vol. , Issue 2002E
[page]

2002
*
Mathematical Reviews
*

*For*example, if the property is that the edges form a

*spanning*

*tree*, then the dispersion

*problem*becomes the max-min

*problem*: Choose p vertices to maximize the weight of the minimum

*spanning*

*tree*on the ...

*Some*

*problems*are apparently considered here

*for*the first time. ...

##
###
Spanning tree with many leaves in quadratic graph

2013
*
International Journal of Research Studies in Computing
*

A polynomial

doi:10.5861/ijrsc.2014.603
fatcat:zemhfmyrlvdxtpatenlqclq22u
*algorithm**for*constructing full*spanning**trees**for*4-regular (Quadratic)*graph*is presented. ...*For*a connected*graph*G let L(G) denote the*maximum*number of leaves in any*spanning**tree*of G. ... A constructive proof that all*graphs*in a particular*class*have*spanning**trees*with at least m leaves becomes an*algorithm*to produce such a*tree**for**graphs*in this*class*. ...##
###
Either/Or: Using Vertex Cover Structure in Designing FPT-Algorithms — the Case of k-Internal Spanning Tree
[chapter]

2003
*
Lecture Notes in Computer Science
*

We show how to use this inherent vertex cover structure to design

doi:10.1007/978-3-540-45078-8_41
fatcat:jhbv4utcinecvbuaegq4dcxryu
*algorithms**for*FPT*problems*, here illustrated mainly by k-*INTERNAL**SPANNING**TREE*. ... In this paper we study the parametric dual of this*problem*, k-*INTERNAL**SPANNING**TREE*(Does G have a*spanning**tree*with at least k*internal*vertices?). ... Acknowledgements: We would like to thank Mike Fellows, Andrzej Proskurowski and Frances Rosamond*for*very helpful conversations and encouragement. ...##
###
Approximation Algorithms for Degree-Constrained Minimum-Cost Network-Design Problems
[chapter]

2009
*
Fundamental Problems in Computing
*

A prototypical example is the degree-constrained node-weighted Steiner

doi:10.1007/978-1-4020-9688-4_9
dblp:conf/birthday/0001MRRH13
fatcat:axlg2cutrvfefon5vphxjv7qp4
*tree**problem*: We are given an undirected*graph*with a non-negative integral function that specifies an upper bound ¥ on the degree ... We study network-design*problems*with two different design objectives: the total cost of the edges and nodes in the network and the*maximum*degree of any node in the network. ... Acknowledgments: We thank the referee*for*several valuable suggestions. We gratefully acknowledge helpful conversations with M. X. Goemans, P. N. Klein, G. Konjevod, S. Krumke, B. Raghavachari, V. S. ...##
###
Blow-Ups, Win/Win's, and Crown Rules: Some New Directions in FPT
[chapter]

2003
*
Lecture Notes in Computer Science
*

This survey reviews the basic notions of parameterized complexity, and describes

doi:10.1007/978-3-540-39890-5_1
fatcat:jojjzpn4fffedjarzcwieynllm
*some*new approaches to designing FPT*algorithms*and*problem*reductions*for**graph**problems*. ... It applies to the following*problem*: Max*Internal**Spanning**Tree*Input: A*graph*G and an integer k; Parameter: k; Question: Does G have a*spanning**tree*with at least k*internal*vertices? ... A win/win approach to designing an FPT*algorithm**for*Max*Internal**Spanning**Tree*has recently been described by Prieto and Sloper [PS03] . ...##
###
Better approximation algorithms for maximum weight internal spanning trees in cubic graphs and claw-free graphs
[article]

2020
*
arXiv
*
pre-print

Given a connected vertex-weighted

arXiv:2006.12561v1
fatcat:mwvikysxifechkxgc2hzfg3eqi
*graph*G, the*maximum*weight*internal**spanning**tree*(MaxwIST)*problem*asks*for*a*spanning**tree*of G that maximizes the total weight of*internal*nodes. ...*For*claw-free*graphs*of degree at least three, we present an*algorithm*that computes a*spanning**tree*whose total*internal*weight is at least 3/5-1/n times the total vertex weight. ... There exists a linear-time 3 4 − -approximation*algorithm**for*the*maximum*weight*internal**spanning**tree**problem*in cubic*graphs*,*for*any > 0. ...##
###
Model-checking for successor-invariant first-order formulas on graph classes of bounded expansion

2017
*
2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
*

In this work we show that the model-checking

doi:10.1109/lics.2017.8005115
dblp:conf/lics/HeuvelKPQRS17
fatcat:jdqaqsza6rgi3ke7ldtaekaj6i
*problem**for*successor-invariant formulas is fixed-parameter tractable on any*class*of finite structures whose underlying Gaifman*graphs*form a*class*of bounded ... It was shown earlier that adding successor-invariance to first-order logic essentially comes at no extra cost*for*the model-checking*problem*on*classes*of finite structures whose underlying Gaifman*graph*... [11] have shown that adding a*spanning**tree*of constant*maximum*degree is enough to be able to interpret*some*successor relation. ...##
###
Model-Checking for Successor-Invariant First-Order Formulas on Graph Classes of Bounded Expansion
[article]

2017
*
arXiv
*
pre-print

In this work we show that the model-checking

arXiv:1701.08516v2
fatcat:pmoy3mbenjchxa6xr6sbapy72y
*problem**for*successor-invariant formulas is fixed-parameter tractable on any*class*of finite structures whose underlying Gaifman*graphs*form a*class*of bounded ... It was shown earlier that adding successor-invariance to first-order logic essentially comes at no extra cost*for*the model-checking*problem*on*classes*of finite structures whose underlying Gaifman*graph*... [11] have shown that adding a*spanning**tree*of constant*maximum*degree is enough to be able to interpret*some*successor relation. ...##
###
Page 7572 of Mathematical Reviews Vol. , Issue 98M
[page]

1998
*
Mathematical Reviews
*

In this paper, we propose an

*algorithm**for*listing all directed*spanning**trees*of G. ... Summary: “A directed*spanning**tree*in a directed*graph*G = (V,A) is a*spanning**tree*such that no two arcs share their tails. ...##
###
Kernelization for Maximum Leaf Spanning Tree with Positive Vertex Weights

2012
*
Journal of Graph Algorithms and Applications
*

a

doi:10.7155/jgaa.00279
fatcat:xesolojekjeuvfvmliovw23qou
*spanning**tree*T*for*G exists such that the combined weight of the leaves of T is at least k. ... In this paper we consider a natural generalization of the wellknown Max Leaf*Spanning**Tree**problem*. ...*for*inspiring me to study*spanning**tree**problems*. ...
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