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A 3/2-Approximation Algorithm for Finding Spanning Trees with Many Leaves in Cubic Graphs [chapter]

Paul Bonsma, Florian Zickfeld
2008 Lecture Notes in Computer Science  
We provide a 3/2-approximation algorithm for this problem when restricted to cubic graphs, improving on the previous 5/3-approximation for this class.  ...  We consider the problem of finding a spanning tree that maximizes the number of leaves (MaxLeaf).  ...  find spanning trees with at least n/3 + 4/3 leaves in graphs with δ ≥ 3.  ... 
doi:10.1007/978-3-540-92248-3_7 fatcat:3pixexls7vh6dopbe3lfe53ssy

A 3/2-Approximation Algorithm for Finding Spanning Trees with Many Leaves in Cubic Graphs

Paul Bonsma, Florian Zickfeld
2011 SIAM Journal on Discrete Mathematics  
We provide a 3/2-approximation algorithm for this problem when restricted to cubic graphs, improving on the previous 5/3-approximation for this class.  ...  We consider the problem of finding a spanning tree that maximizes the number of leaves (MaxLeaf).  ...  find spanning trees with at least n/3 + 4/3 leaves in graphs with δ ≥ 3.  ... 
doi:10.1137/100801251 fatcat:5kct7e6r6jdspct3lkiuinmzdu

A 5/3-Approximation for Finding Spanning Trees with Many Leaves in Cubic Graphs [chapter]

José R. Correa, Cristina G. Fernandes, Martín Matamala, Yoshiko Wakabayashi
Approximation and Online Algorithms  
For a connected graph G, let L(G) denote the maximum number of leaves in a spanning tree in G. The problem of computing L(G) is known to be NP-hard even for cubic graphs.  ...  We improve on Loryś and Zwoźniak's result presenting a 5/3-approximation for this problem on cubic graphs.  ...  Acknowledgements The authors would like to thank the referees for their comments and suggestions.  ... 
doi:10.1007/978-3-540-77918-6_15 dblp:conf/waoa/CorreaFMW07 fatcat:oy5qgr2qnfdkhbulrr7cgjieje

Graph-TSP from Steiner Cycles [chapter]

Satoru Iwata, Alantha Newman, R. Ravi
2014 Lecture Notes in Computer Science  
For a graph G, if we can find a spanning tree T and a simple cycle that contains the vertices with odd-degree in T , then we show how to combine the classic "double spanning tree" algorithm with Christofides  ...  Since a Hamiltonian path is a spanning tree with two leaves, this motivates the question of whether or not a graph containing a spanning tree with few leaves has a short TSP tour.  ...  Acknowledgements We would like to thank the anonymous referees for many useful comments.  ... 
doi:10.1007/978-3-319-12340-0_26 fatcat:vf4loavsyvaxvjnxnemxnmnu7a

Graph-TSP from Steiner Cycles [article]

Satoru Iwata, Alantha Newman, R. Ravi
2014 arXiv   pre-print
For a graph G, if we can find a spanning tree T and a simple cycle that contains the vertices with odd-degree in T, then we show how to combine the classic "double spanning tree" algorithm with Christofides  ...  Since a Hamiltonian path is a spanning tree with two leaves, this motivates the question of whether or not a graph containing a spanning tree with few leaves has a short TSP tour.  ...  Acknowledgements We would like to thank the anonymous referees for many useful comments.  ... 
arXiv:1407.2844v1 fatcat:226bop5yvreftcyqmbqoixqle4

Hardness and approximation results for Black Hole Search in arbitrary networks

Ralf Klasing, Euripides Markou, Tomasz Radzik, Fabiano Sarracco
2007 Theoretical Computer Science  
A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node without leaving any trace.  ...  Our algorithm follows a natural approach of exploring networks via spanning trees. We prove that this approach cannot lead to an approximation ratio bound better than 3/2.  ...  Acknowledgements We would like to thank the two anonymous referees for their very helpful comments and suggestions.  ... 
doi:10.1016/j.tcs.2007.04.024 fatcat:5hwhauwjfzf7bpkzlkut5myn64

Unknotted Strand Routings of Triangulated Meshes [chapter]

Abdulmelik Mohammed, Mustafa Hajij
2017 Lecture Notes in Computer Science  
In this paper, we present a cubic-time 5 3approximation algorithm to compute unknotted Chinese-postman scaffold routings on triangulated orientable surfaces of higher genus.  ...  In molecular self-assembly such as DNA origami, a circular strand's topological routing determines the feasibility of a design to assemble to a target.  ...  Moreover, it is a 5 3approximation algorithm for UCPT. Proof. LetT be the outputted non-crossing Chinese postman tour on H.  ... 
doi:10.1007/978-3-319-66799-7_4 fatcat:jbdm7dxgs5ddnco7ul7dgwpvqu

Design and Analysis of Randomized and Approximation Algorithms (Dagstuhl Seminar 11241)

Martin Dyer, Uriel Feige, Alan M. Frieze, Marek Karpinski, Marc Herbstritt
2011 Dagstuhl Reports  
Nevertheless, practical necessity dictates that acceptable solutions be found in a reasonable time.  ...  Thanks go to Mathias Hauptmann for his help in collecting abstracts of the talks and other related materials for these Proceedings.  ...  A (5/3 + )-Approximation for Strip Packing Lars Prädel (University of Kiel, DE) License Creative Commons BY-NC-ND 3.0 Unported license © Lars Prädel We study strip packing, which is one of the most  ... 
doi:10.4230/dagrep.1.6.24 dblp:journals/dagstuhl-reports/DyerFFK11 fatcat:lb4xum4yizgo5iwrwau7d5csiy

On the complexity of barrier resilience for fat regions and bounded ply

Matias Korman, Maarten Löffler, Rodrigo I. Silveira, Darren Strash
2018 Computational geometry  
We also show 12 that the problem is fixed-parameter tractable (FPT) for unit disks and 13 for similarly-sized β-fat regions with bounded ply ∆ and O(1) pairwise 14 boundary intersections.  ...  5 In the barrier resilience problem (introduced by Kumar et al., Wire-6 less Networks 2007), we are given a collection of regions of the plane, 7 acting as obstacles, and we would like to remove the minimum  ...  There has been partial progress towards settling the question: Bereg 8 and Kirkpatrick [3] present a factor 5/3-approximation algorithm for the unit 9 disk case.  ... 
doi:10.1016/j.comgeo.2018.02.006 fatcat:hmxbuwx6qnfn3hr4m3ctjpsoyi

On the Complexity of Barrier Resilience for Fat Regions [article]

Matias Korman, Maarten Löffler, Rodrigo I. Silveira, Darren Strash
2017 arXiv   pre-print
We also show that the problem is fixed-parameter tractable (FPT) for unit disks and for similarly-sized β-fat regions with bounded ply Δ and O(1) pairwise boundary intersections.  ...  In the barrier resilience problem (introduced by Kumar et al., Wireless Networks 2007), we are given a collection of regions of the plane, acting as obstacles, and we would like to remove the minimum number  ...  The authors would like to thank some anonymous referees for their thorough check of a previous version of this document. M.K was partially supported by the ELC project (MEXT KAKENHI No. 24106008).  ... 
arXiv:1302.4707v5 fatcat:of422ralojfvpbgf6l7dygna4q

Geometric and Combinatorial Structures on Graphs [article]

Florian Zickfeld, Technische Universität Berlin, Technische Universität Berlin, Stefan Felsner
2008
The thesis is concerned with four main topics: connection of Schnyder woods and orthogonal surfaces, the number of planar orientations with prescribed out-degrees, spanning trees with many leaves, and  ...  Coplanar orthogonal surfaces are in correspondence with a large class of convex straight line drawings of 3-connected planar graphs.  ...  A 2-approximation is given in [85] , and when the input is restricted to cubic graphs, the current best approximation is a 5/3-approximation [27] .  ... 
doi:10.14279/depositonce-1750 fatcat:uo6kuvovzrhabbjx53ltpdfrke

Scientific Visualization (Dagstuhl Seminar 11231) Outdoor and Large-Scale Real-World Scene Analysis. 15th Workshop Theoretic Foundations of Computer Vision

Min Chen, Hans Hagen, Charles Hansen, Arie Kaufman, Martin Dyer, Uriel Feige, Alan Frieze, Marek Karpinski, Frank Dellaert, Jan-Michael Frahm, Marc Pollefeys, Bodo Rosenhahn
2011 unpublished
Thanks go to Mathias Hauptmann for his help in collecting abstracts of the talks and other related materials for these Proceedings.  ...  We thank Annette Beyer and Angelika Mueller-von Brochowski for their continuous support and help in organizing this workshop.  ...  Szabo A disconnected graph G does not contain any spanning trees.  ... 
fatcat:jzxttttmrvda3caw6dy4q2kw6i

Approximation techniques for unsplittable flow and traveling salesmen problems

Zachary Friggstad
2011
These results are extended to many other variants of finding multiple paths in metrics whose union spans all nodes.  ...  We then further generalize the problem and study the problem of finding up to k paths with minimum total distance in an asymmetric metric such that the union of these paths spans all nodes.  ...  In the case that both endpoints are specified, a 5 3 -approximation is shown.  ... 
doi:10.7939/r3qs8b fatcat:4pirci63izapfbc4ha6dtbw47i

On building and comparing trees Application to supertrees in phylogenetics

Vincent Berry, Vincent, Académie De Montpellier
2009 unpublished
Bininda-Emonds, and an anonymous reviewer for many invaluable remarks on a first version of this manuscript. This work has been supported by the "ACI Informatique  ...  Additionally, they proved that the MAST problem is NP-Hard for three trees of unbounded degree and gave an O(kn 5 ) 3-approximation algorithm for the problem.  ...  trees a tree with leaves spanning most input trees, that they call a seed tree.  ... 
fatcat:kzulocavzjac5htps7gbmmoyk4

Overcoming Hurdles in Downstream Processing of Tobacco-derived Biopharmaceutical Proteins

Johannes Felix Buyel
2017
Anzahl pflanzlich hergestellter Proteine in klinischen Phasen getestet und letztlich auch in den Markt eintreten werden.  ...  Trotzdem ist in den letzten Jahren festzustellen, dass das Interesse an Biopharmazeutika, die in Pflanzen produziert wurden, steigt.  ...  for system disassembly [person- hours] 6 1 1 11 2 3 5 1 1 1 Total labor time [person- hours] 36 5 5 60 8 15 31 5 5 3 Approximate space requirement for support equipment  ... 
doi:10.5445/ir/1000077007 fatcat:asqtt7t57zafljrnelfdmgnn7i