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An exact algorithm for the Maximum Leaf Spanning Tree problem

2011
*
Theoretical Computer Science
*

Given

doi:10.1016/j.tcs.2011.07.011
fatcat:3yhdim7mjvgdtftxgjjchcbqnm
*an*undirected graph with n vertices,*the**Maximum**Leaf**Spanning**Tree**problem*is to find a*spanning**tree*with as many leaves as possible. ... Finally, we provide a lower bound of Ω(1.4422 n )*for**the*worst case running time of our*algorithm*. ... Generating*the*recurrences*For**the*interested reader, we provide in this appendix some AMPL code used to solve some of*the*recurrences given in Section 5. ...##
###
An Exact Algorithm for the Maximum Leaf Spanning Tree Problem
[chapter]

2009
*
Lecture Notes in Computer Science
*

Given

doi:10.1007/978-3-642-11269-0_13
fatcat:qucdqar7vbdnhez2hu37eagtoy
*an*undirected graph with n nodes,*the**Maximum**Leaf**Spanning**Tree**problem*is to find a*spanning**tree*with as many leaves as possible. ... Finally we provide a lower bound of Ω(1.4422 n )*for**the*worst case running time of our*algorithm*. ... Fig. 1 . 1*An**algorithm**for**Maximum**Leaf**Spanning**Tree*. ...##
###
An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem

2012
*
Journal of Discrete Algorithms
*

NP-hard

doi:10.1016/j.jda.2012.03.006
fatcat:uwa6o6dflfaifdmbpxb6s2detu
*problems*on directed graphs Outbranching with a*maximum*number of leaves Given a directed graph G = (V , A),*the*Directed*Maximum**Leaf**Spanning**Tree**problem*asks to compute a directed*spanning*... We also provide*an*example showing a lower-bound*for**the*running time of our*algorithm*. ... Since G t has n t = 3t + 2 many vertices,*the*result follows. 2 Conclusions and future work*The*paper at hand presented*an**algorithm*which solves*the*Directed*Maximum**Leaf**Spanning**Tree**problem*in time ...##
###
Minimum Connected Dominating Set for Certain Circulant Networks

2015
*
Procedia Computer Science
*

In general,

doi:10.1016/j.procs.2015.07.401
fatcat:w2bu3v66cja23oullt52k7xt7y
*the**problem*is proved to be NP-hard. In this paper we find a Minimum Connected Dominating Set*for*certain Circulant Networks. ... A Minimum Connected Dominating Set is a minimum set of connected nodes such that every other node in*the*network is one hop connected with a node in this set. ... Conclusion In this paper we calculated*the**exact*value*for*Minimum Dominating Set and Minimum Connected Dominating Set, thereby solving*Maximum**Leaf**Spanning**Tree**problem**for*certain Circulant Networks ...##
###
Computing and maximizing the exact reliability of wireless backhaul networks

2018
*
Electronic Notes in Discrete Mathematics
*

*The*

*algorithm*computes a conditional probability

*tree*, where each

*leaf*in

*the*

*tree*requires a valid routing

*for*

*the*network. ... Any such

*tree*provides

*an*upper and lower bound on

*the*reliability, and

*the*

*algorithm*improves these bounds by branching in

*the*

*tree*. ...

*For*2-cycles instance, our proposed

*algorithm*solves

*the*

*problem*

*for*all budgets in less than a minute, requiring between 34 to 81 iterations to compute

*the*

*exact*reliability. ...

##
###
Finding the Optimal Nets for Self-Folding Kirigami

2018
*
Physical Review Letters
*

Identifying

doi:10.1103/physrevlett.120.188001
pmid:29775357
fatcat:3wn7mlm3mzdvbfhze5kkpkjxeu
*the*nets that maximize*the*number of vertex connections corresponds to finding*the*set of*maximum**leaf**spanning**trees*of*the*shell graph. ... This method allows not only to design*the*self-assembly of much larger shell structures but also to apply additional design criteria, as a complete catalog of*the**maximum**leaf**spanning**trees*is obtained ...*The**exact*number L depends on*the*details of*the*graph, and its determination requires to actually solve*the**maximum**leaf**spanning**tree**problem*. ...##
###
Fixed Parameter Evolutionary Algorithms and Maximum Leaf Spanning Trees: A Matter of Mutation
[chapter]

2010
*
Parallel Problem Solving from Nature, PPSN XI
*

We investigate

doi:10.1007/978-3-642-15844-5_21
dblp:conf/ppsn/KratschLNO10
fatcat:byxjfluezzgydcmzdrxqmcskda
*the*NP-hard*problem*of computing a*spanning**tree*that has a maximal number of leaves by evolutionary*algorithms*in*the*context of fixed parameter tractability (FPT) where*the**maximum*number ... Evolutionary*algorithms*have been shown to be very successful*for*a wide range of NP-hard combinatorial optimization*problems*. ... FPT of Edge Exchanges In this section we prove that*Algorithm*2 is*an*FPT*algorithm**for**the**maximum**leaf**spanning**tree**problem*with respect to*the*maximal number of leaves k. ...##
###
On the complexity of energy efficient pairwise calibration in embedded sensors

2013
*
Applied Soft Computing
*

*an*NP-complete

*problem*. ... We also conducted heuristic tests using genetic

*algorithm*to solve

*the*optimization version of

*the*

*problem*, on various graphs. ...

*An*iteration path

*for*calibration of a sensor j is defined as

*the*path from

*the*root to sensor j on

*the*

*spanning*

*tree*. ...

##
###
A Faster Exact Algorithm for the Directed Maximum Leaf Spanning Tree Problem
[article]

2009
*
arXiv
*
pre-print

Given a directed graph G=(V,A),

arXiv:0911.1900v2
fatcat:ydx2kk6an5acfnnjjmsn62mfwi
*the*Directed*Maximum**Leaf**Spanning**Tree**problem*asks to compute a directed*spanning**tree*(i.e.,*an*out-branching) with as many leaves as possible. ... By designing a Branch-and-Reduced*algorithm*combined with*the*Measure & Conquer technique*for*running time analysis, we show that*the**problem*can be solved in time ^*(1.9043^n) using polynomial space. ... Thomassé [4] described a 92-approximation*algorithm*together with*an*O(k 2 )kernel*for**the*Directed*Maximum**Leaf**Spanning**Tree**problem*. ...##
###
Foreword

2009
*
Computational Management Science
*

of

doi:10.1007/s10287-009-0114-7
fatcat:6kf6njz6erhqbj2u33g5lefege
*exact*and heuristic*algorithms**for**the*effective solution of hard*problems*. ... His worst-case performance guarantee heuristic*algorithm**for**the*Travelling Salesman*Problem*is a groundbreaking work and, although never published in*an*international journal, collected*an*impressive ... In*the*following paper, "Reformulations and Solution*Algorithms**for**the**Maximum**Leaf**Spanning**Tree**Problem*", by Abilio Lucena, Nelson Maculan and Luidi Simonetti,*the*authors tackle*the*NP-hard*Maximum*...##
###
Reload cost problems: minimum diameter spanning tree

2001
*
Discrete Applied Mathematics
*

We consider

doi:10.1016/s0166-218x(00)00392-9
fatcat:nbung2c6h5dxhkhgjzamyop5fu
*the**problem*of ÿnding a*spanning**tree*of minimum diameter with respect to*the*reload costs. We present lower bounds*for**the*approximability even on graphs with*maximum*degree 5. ... On*the*other hand we provide*an**exact**algorithm**for*graphs of*maximum*degree 3. ? (J. Ste*an*). 0166-218X/01/$ -see front matter ? 2001 Elsevier Science B.V. All rights reserved. ...*Exact*solution*for*graphs with*maximum*degree 3 In this section we provide*an**exact**algorithm**for*graphs with*maximum*degree 3. ...##
###
Incremental algorithms for the maximum internal spanning tree problem

2021
*
Science China Information Sciences
*

*The*

*maximum*internal

*spanning*

*tree*(MIST)

*problem*is utilized to determine a

*spanning*

*tree*in a graph G, with

*the*

*maximum*number of possible internal vertices. ... We first obtained

*an*IMIST

*algorithm*with a competitive ratio of 2, followed by a 12/7-competitive

*algorithm*based on

*an*approximation

*algorithm*

*for*MIST. ... In

*the*following, we present

*the*

*exact*

*algorithm*and analyze its competitive ratio. Let T be

*an*r-approximate

*maximum*internal

*spanning*

*tree*. ...

##
###
Integer programming approach for directed minimum spanning tree problem on temporal graphs

2016
*
Proceedings of the 1st ACM SIGMOD Workshop on Network Data Analytics - NDA '16
*

In this paper, we explore

doi:10.1145/2980523.2980528
dblp:conf/sigmod/IkutaA16
fatcat:2mra2dfpsfejbld5a6znj6c7ta
*the*minimum-weight*spanning**tree**problem*on temporal graphs, which was recently proposed by Huang et al. [SIGMOD 2015]. ... Even*the*most fundamental*problems**for*static graphs become nontrivial*for*temporal graphs. ... Our Contribution We propose*an**exact**algorithm**for**the*minimum directed*spanning**tree**problem*, while existing methods focus on obtaining*an*approximate solution. ...##
###
On the analysis of the (1+1) evolutionary algorithm for the maximum leaf spanning tree problem

2014
*
International Journal of Computer Mathematics
*

A lot of heuristic

doi:10.1080/00207160.2014.964695
fatcat:gpdlr2wlavhe7hk5tydjt3w24m
*algorithms*, such as Evolutionary*algorithms*(EAs), are used to solve*the**maximum**leaf**spanning**tree*(MLST)*problem*which is non-deterministic polynomial time hard (NP-hard). ... Furthermore, we reveal that*the*(1 + 1) EA can outperform*the*local search*algorithms*on two instances of*the*MLST*problem*. ... Acknowledgements*The*authors thank*the*anonymous reviewers and*the*editor*for*their valuable comments and suggestions that help improve this paper. ...##
###
Page 5850 of Mathematical Reviews Vol. , Issue 2004g
[page]

2004
*
Mathematical Reviews
*

90035 05C85
Fujie, Tetsuya

*An**exact**algorithm**for**the**maximum**leaf**spanning**tree**problem*. ... Summary: “Given a connected graph,*the**maximum**leaf**spanning**tree**problem*(MLSTP) is to find a*spanning**tree*whose number of leaves (degree-one vertices) is*maximum*. ...
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