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Better Algorithms and Bounds for Directed Maximum Leaf Problems [article]

Noga Alon, Fedor V. Fomin, Gregory Gutin, Michael Krivelevich, Saket Saurabh
2007 arXiv   pre-print
The Directed Maximum Leaf Out-Branching problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves.  ...  In this paper, we improve known parameterized algorithms and combinatorial bounds on the number of leaves in out-branchings.  ...  Discussion and Open Problems In this paper, we continued algorithmic and combinatorial investigation of the Directed Maximum Leaf Out-Branching problem.  ... 
arXiv:0707.1095v1 fatcat:vkb6mlq63zdtjjah3mpzt7y2hi

Better Algorithms and Bounds for Directed Maximum Leaf Problems [chapter]

Noga Alon, Fedor V. Fomin, Gregory Gutin, Michael Krivelevich, Saket Saurabh
2007 Lecture Notes in Computer Science  
The Directed Maximum Leaf Out-Branching problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves.  ...  In this paper, we improve known parameterized algorithms and combinatorial bounds on the number of leaves in out-branchings.  ...  Discussion and Open Problems In this paper, we continued the algorithmic and combinatorial investigation of the Directed Maximum Leaf Out-Branching problem.  ... 
doi:10.1007/978-3-540-77050-3_26 fatcat:pyird5xdsjgeznibl5n55774ye

A Strengthened Branch and Bound Algorithm for the Maximum Common (Connected) Subgraph Problem [article]

Jianrong Zhou and Kun He and Jiongzhi Zheng and Chu-Min Li and Yanli Liu
2022 arXiv   pre-print
We propose a new and strengthened Branch-and-Bound (BnB) algorithm for the maximum common (connected) induced subgraph problem based on two new operators, Long-Short Memory (LSM) and Leaf vertex Union  ...  Given two graphs for which we search for the maximum common (connected) induced subgraph, the first operator of LSM maintains a score for the branching node using the short-term reward of each vertex of  ...  , we address the Maximum Common induced Subgraph (MCS) and Maximum Common Connected induced Subgraph (MCCS) problems, and we propose an effective Branch-and-Bound (BnB) algorithm called McSplit+LL for  ... 
arXiv:2201.06252v1 fatcat:e5t4qyvmqnedbkv5x2stey4p34

Parameterized Algorithms for Directed Maximum Leaf Problems [article]

Noga Alon, Fedor Fomin, Gregory Gutin, Michael Krivelevich, Saket Saurabh
2007 arXiv   pre-print
Our algorithms are based on the following combinatorial result which can be viewed as a generalization of many results for a 'spanning tree with many leaves' in the undirected case, and which is interesting  ...  This settles completely an open question of Fellows and solves another one for digraphs in L.  ...  We thank Bruno Courcelle, Martin Grohe, Eun Jung Kim and Stephan Kreutzer for useful discussions of the paper.  ... 
arXiv:cs/0702049v1 fatcat:6ly6553a25azhalba7h5zckhmi

Leafy Spanning Arborescences in DAGs [article]

Cristina G. Fernandes, Carla N. Lintzmayer
2020 arXiv   pre-print
We also adapt a result for the undirected case and derive an inapproximability result for the vertex-weighted version of Maximum Leaf Spanning Arborescence on rooted directed acyclic graphs.  ...  We consider the subjacent problem of, given a directed graph D, finding a spanning arborescence of D, if one exists, with the maximum number of leaves.  ...  Is it possible to extend our approximation or any greedy algorithm for Maximum Leaf Spanning Arborescence to address directed graphs with bounded directed tree width?  ... 
arXiv:2007.07660v1 fatcat:lhirviy7inb5pmaxwlyslcuw6i

Meet and merge: Approximation algorithms for confluent flows

Jiangzhuo Chen, Rajmohan Rajaraman, Ravi Sundaram
2006 Journal of computer and system sciences (Print)  
This implies an O( √ n) approximation algorithm for the problem.  ...  We also establish a lower bound on the gap between confluent and splittable flows, and consider multicommodity and fractional versions of confluent flow problems.  ...  . • We provide optimal polynomial-time algorithms for the multi-sink single commodity problem (with arbitrary supplies) for both undirected and directed trees.  ... 
doi:10.1016/j.jcss.2005.09.009 fatcat:qihcnp5govcslbn2e4xf54m3ca

Meet and merge

Jiangzhuo Chen, Rajmohan Rajaraman, Ravi Sundaram
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
This implies an O( √ n) approximation algorithm for the problem.  ...  We also establish a lower bound on the gap between confluent and splittable flows, and consider multicommodity and fractional versions of confluent flow problems.  ...  . • We provide optimal polynomial-time algorithms for the multi-sink single commodity problem (with arbitrary supplies) for both undirected and directed trees.  ... 
doi:10.1145/780596.780598 fatcat:2ksyvlq4orhl3d4oobjeihlh4u

Meet and merge

Jiangzhuo Chen, Rajmohan Rajaraman, Ravi Sundaram
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
This implies an O( √ n) approximation algorithm for the problem.  ...  We also establish a lower bound on the gap between confluent and splittable flows, and consider multicommodity and fractional versions of confluent flow problems.  ...  . • We provide optimal polynomial-time algorithms for the multi-sink single commodity problem (with arbitrary supplies) for both undirected and directed trees.  ... 
doi:10.1145/780542.780598 dblp:conf/stoc/ChenRS03 fatcat:com5rwogdfbjfod3ogxaavio2m

Optimal Agreement Supertrees [chapter]

David Bryant
2001 Lecture Notes in Computer Science  
We present polynomial time algorithms for computing an optimal agreement supertree, if one exists, of a bounded number of binary trees.  ...  The criteria of optimality can be one of four standard phylogenetic criteria: binary character compatibility; maximum summed quartet weight; ordinary least squares; and minimum evolution.  ...  Acknowledgements We wish to thank an anonymous referee for their helpful comments and suggestions.  ... 
doi:10.1007/3-540-45727-5_3 fatcat:2cb4tv2qenge5nlcskzwsft3vm

A New Algorithm for Finding Trees with Many Leaves

Joachim Kneis, Alexander Langer, Peter Rossmanith
2010 Algorithmica  
These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf Out-Tree and Directed Maximum Leaf Spanning Out-Tree in the case of directed graphs  ...  Currently, the fastest algorithms for these problems have run times of O(poly(n) + 6.75 k poly(k)) and 2 O(k log k) poly(n), respectively.  ...  In the area of parameterized algorithms, the Maximum Leaf Spanning Tree problem is very prominent.  ... 
doi:10.1007/s00453-010-9454-5 fatcat:5qugeknifvcjfkaludmqdelviq

A New Algorithm for Finding Trees with Many Leaves [chapter]

Joachim Kneis, Alexander Langer, Peter Rossmanith
2008 Lecture Notes in Computer Science  
These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf Out-Tree and Directed Maximum Leaf Spanning Out-Tree in the case of directed graphs  ...  Currently, the fastest algorithms for these problems have run times of O(poly(n) + 6.75 k poly(k)) and 2 O(k log k) poly(n), respectively.  ...  In the area of parameterized algorithms, the Maximum Leaf Spanning Tree problem is very prominent.  ... 
doi:10.1007/978-3-540-92182-0_26 fatcat:ybz3jyjkjraiba7wpnnoslicwu

Towards Fully Multivariate Algorithmics: Some New Results and Directions in Parameter Ecology [chapter]

Michael Fellows
2009 Lecture Notes in Computer Science  
parameterized complexity and algorithmics -itself a natural two-dimensional generalization of the familiar one-dimensional framework of P versus N P.  ...  This paper reports on three recent research directions that begin to explore the subject of fully multivariate algorithmics, meaning by this the largely uncharted theoretical landscape that lies beyond  ...  Many thanks to Frances Rosamond for conversations and assistance with this paper, and the invited talk at IWOCA 2009 on which it is based.  ... 
doi:10.1007/978-3-642-10217-2_2 fatcat:ig7hd6suh5cuvb5kcohijegkim

Grooming of dynamic traffic in WDM star and tree networks using a genetic algorithm

Kun-Hong Liu, Yong Xu, De-Shuang Huang, Min Cheng
2007 Photonic network communications  
To evaluate the algorithm, tighter bounds are derived. Computer simulation results show that our algorithm is efficient in reducing both the numbers of ADM's and wavelengths in tree and star networks.  ...  A genetic algorithm (GA) based approach is proposed to support arbitrary dynamic traffic patterns, which minimizes the number of ADM's and wavelengths.  ...  bounds; (d) The number of wavelengths vs. nodes for g=24 along with upper bounds; (e) The number of ADM's vs. nodes for g=24 along with lower bounds and maximum traffic matrices; (f) The number of wavelengths  ... 
doi:10.1007/s11107-007-0103-0 fatcat:3ctdnesxgndxbcxydllqwkk7l4

Lower Bounds for Maximum Parsimony with Gene Order Data [chapter]

Abraham Bachrach, Kevin Chen, Chris Harrelson, Radu Mihaescu, Satish Rao, Apurva Shah
2005 Lecture Notes in Computer Science  
In this paper, we study lower bound techniques for branchand-bound algorithms for maximum parsimony, with a focus on gene order data.  ...  We give a simple O(n 3 ) time dynamic programming algorithm for computing the maximum circular ordering lower bound, where n is the number of leaves.  ...  Acknowledgements We thank Bernard Moret for helpful discussions and Jijun Tang for sharing his code with us.  ... 
doi:10.1007/11554714_1 fatcat:a2nhveec25djtcgpgyqauez4fe

Local algorithms in (weakly) coloured graphs [article]

Matti Åstrand, Valentin Polishchuk, Joel Rybicki, Jukka Suomela, Jara Uitto
2010 arXiv   pre-print
We also give a matching lower bound proving that there is no local algorithm with a better approximation factor for either of these problems.  ...  We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in 2-coloured and weakly 2-coloured graphs.  ...  Acknowledgements This work was supported in part by the Academy of Finland, Grants 116547, 118653 (ALGODAN), and 132380, by Helsinki Graduate School in Computer Science and Engineering (Hecse), and by  ... 
arXiv:1002.0125v1 fatcat:tdf4ic6wmjf65l5xrkwnyr2ira
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