Packing algorithms for arborescences (and spanning trees) in capacitated graphs

To cite this version:Mourad Baïou, Fancisco Barahona. A linear programming approach to increasing the weight of all minimum spanning trees. CECO-889. 2005 Abstract:Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. We formulate this as a combinatorial linear program and give an algorithm. Mots clés :Arbres couvrants de poids minimum, sécurisation des réseaux.Key Words : Minimum weight spanning trees, packing spanning trees, network reinforcement, strength problem.y Classification AMS:1 Laboratoire d'Econométrie, CNRS et Ecole polytechnique. A LINEAR PROGRAMMING APPROACH TO INCREASING THE WEIGHT OF ALL MINIMUM SPANNING TREESMOURAD BAÏOU AND FRANCISCO BARAHONA Abstract. Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. We formulate this as a combinatorial linear program and give an algorithm.

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“…The last two references give O(n 4 ) algorithms. For the dual problem (26)-(28) O(n 5 ) algorithms have been given in [2] and [8].…”

Section: Increasing the Weight Of Mwsts: A Linear Programmentioning

confidence: 99%

A linear programming approach to increasing the weight of all minimum spanning trees

Baı̈ou

Barahona

2008

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“…The formulated problem can be considered as maximum packing of directed rooted spanning trees in a graph. There exists a polynomial time algorithm providing optimal solution to this problem based on [27] as can be found in [28]. However, the problem in the general non-spanning case, where D ⊂ N − {s} ), is NP-Hard.…”

Section: (G) Further Refinement Of This Observation Comes Frommentioning

confidence: 99%

Fast replication in content distribution overlays

Ganguly

Saxena

Bhatnagar

et al.

Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies.

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Abstract-We present SPIDER -a system for fast replication or distribution of large content from a single source to multiple sites interconnected over Internet or via a private network. In order to exploit spatial diversity of the underlying network, SPIDER uses an overlay structure composed of dedicated Transit Nodes (TNs). The data transport mechanism in SPIDER leverages this overlay structure to provide a coordinated approach that minimizes the maximum time to replicate to all destination sites (the makespan of content replication). In order to achieve this objective, SPIDER employs two orthogonal components: a) creation of multiple dynamic distribution trees using the transit nodes b) end-to-end reliable data transport with flow control on these trees by chaining point-to-point TCPs. We further present simulations based results to quantify benefits of tree construction algorithms in random topologies. We evaluate the real implementation of the SPIDER in PlanetLab and observe a 2-6 times speed up compared to different existing schemes.

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“…Seja também r um vértice de D. Edmonds [Edm73] estabeleceu que o sistema capacitado e irrestrito de núcleos D := (V(r), A, δ , c) empacota. Gabow e Manu [GM98] provaram o seguinte teorema que garante a existência de um empacotamento com poucas coberturas. Teorema 1.7 (Gabow e Manu [GM98]) Seja D = (V, A) um digrafo, c : A → R + uma função capacidade, e r um vértice de D. Então (V(r), A, δ , c) possui um empacotamento y tal que…”

Section: Sistemas Capacitados E Irrestritos De Núcleosunclassified

“…É conveniente, agora, discutir brevemente e de forma superficial, um algoritmo de Gabow e Manu [GM98] para o empacotamento fracionário de arborescências geradoras, uma vez que tal algoritmo será generalizado neste trabalho. Ressaltamos que este algoritmo foi estendido por Barahona [Bar04] para o problema do empacotamento fracionário de T -junções e, por Matsuoka [Mat12], para o problema do empacotamento fracionário em clutters ideais.…”

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Um arcabouço generalizado para empacotamento de ramificações e outras estruturas combinatórias

Rey¹

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Packing algorithms for arborescences (and spanning trees) in capacitated graphs

Cited by 30 publications

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A linear programming approach to increasing the weight of all minimum spanning trees

A linear programming approach to increasing the weight of all minimum spanning trees

Fast replication in content distribution overlays

Um arcabouço generalizado para empacotamento de ramificações e outras estruturas combinatórias

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