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### An exact algorithm for the Maximum Leaf Spanning Tree problem

Henning Fernau, Joachim Kneis, Dieter Kratsch, Alexander Langer, Mathieu Liedloff, Daniel Raible, Peter Rossmanith
2011 Theoretical Computer Science
Given 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]

Henning Fernau, Joachim Kneis, Dieter Kratsch, Alexander Langer, Mathieu Liedloff, Daniel Raible, Peter Rossmanith
2009 Lecture Notes in Computer Science
Given 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

Daniel Binkele-Raible, Henning Fernau
2012 Journal of Discrete Algorithms
NP-hard 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

N. Parthiban, Indra Rajasingh, R. Sundara Rajan
2015 Procedia Computer Science
In general, 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

David Coudert, James Luedtke, Eduardo Moreno, Konstantinos Priftis
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

N. A. M. Araújo, R. A. da Costa, S. N. Dorogovtsev, J. F. F. Mendes
2018 Physical Review Letters
Identifying 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]

Stefan Kratsch, Per Kristian Lehre, Frank Neumann, Pietro Simone Oliveto
2010 Parallel Problem Solving from Nature, PPSN XI
We investigate 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

Hüseyin Akcan
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]

Daniel Raible, Henning Fernau
2009 arXiv   pre-print
Given a directed graph G=(V,A), 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  described a 92-approximation algorithm together with an O(k 2 )kernel for the Directed Maximum Leaf Spanning Tree problem.  ...

### Foreword

Paolo Toth
2009 Computational Management Science
of 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

Hans-Christoph Wirth, Jan Steffan
2001 Discrete Applied Mathematics
We consider 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

Xianbin Zhu, Wenjun Li, Yongjie Yang, Jianxin Wang
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

Takuto Ikuta, Takuya Akiba
2016 Proceedings of the 1st ACM SIGMOD Workshop on Network Data Analytics - NDA '16
In this paper, we explore 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

Xiaoyun Xia, Yuren Zhou, Xinsheng Lai
2014 International Journal of Computer Mathematics
A lot of heuristic 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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