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One Tree Suffices: A Simultaneous O(1)Approximation for SingleSink BuyatBulk
, 2012
"... We study the singlesink buyatbulk problem with an unknown cost function. We wish to route flow from a set of demand nodes to a root node, where the cost of routing x total flow along an edge is proportional to f (x) for some concave, nondecreasing function f satisfying f (0) = 0. We present a ..."
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We study the singlesink buyatbulk problem with an unknown cost function. We wish to route flow from a set of demand nodes to a root node, where the cost of routing x total flow along an edge is proportional to f (x) for some concave, nondecreasing function f satisfying f (0) = 0. We present a
From Uncertainty to NonLinearity: Solving Virtual Private Network via SingleSink BuyatBulk
"... The virtual private network problem (Vpn) models scenarios where traffic is uncertain or rapidly changing. The goal is supporting at minimum cost a given family of traffic matrices, which are implicitly given by upper bounds on the ingoing and outgoing traffic at each node. Costs are classically def ..."
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build upon a novel reduction, based on Kőnig’s theorem, which allows us to turn uncertainty of traffic into nonlinearity of the objective function. This way, we are able to reduce linear Vpn and concave Vpn to the singlesink rentorbuy problem (Srob) and the singlesink buyatbulk problem (Ssbb
An Oblivious Spanning Tree for SingleSink BuyatBulk In Low Doublingdimension Graphs
"... We consider the problem of constructing a single spanning tree for the singlesink buyatbulk network design problem for doublingdimension graphs. We compute a spanning tree to route a set of demands along a graph G to or from a designated sink node. The demands could be aggregated at (or symmetr ..."
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We consider the problem of constructing a single spanning tree for the singlesink buyatbulk network design problem for doublingdimension graphs. We compute a spanning tree to route a set of demands along a graph G to or from a designated sink node. The demands could be aggregated at (or
BuyatBulk Network Design with Protection
"... We consider approximation algorithms for buyatbulk network design, with the additional constraint that demand pairs be protected against edge or node failures in the network. In practice, the most popular model used in high speed telecommunication networks for protection against failures, is the s ..."
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Cited by 11 (0 self)
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, is the socalled 1+1 model. In this model, two edge or nodedisjoint paths are provisioned for each demand pair. We obtain the first nontrivial approximation algorithms for buyatbulk network design in the 1+1 model for both edge and nodedisjoint protection requirements. Our results are for the single
Simultaneous Optimization for Concave Costs: Single Sink Aggregation or Single Source BuyatBulk
 In Proc. of the 14 th Symposium on Discrete Algorithms (SODA
, 2003
"... We consider the problem of finding efficient trees to send information from k sources to a single sink in a network where information can be aggregated at intermediate nodes in the tree. Specifically, we assume that if information from j sources is traveling over a link, the total information tha ..."
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Cited by 120 (3 self)
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that needs to be transmitted is f(j). One natural and important (though not necessarily comprehensive) class of functions is those which are concave, nondecreasing, and satisfy f(0) = 0. Our goal is to find a tree which is a good approximation simultaneously to the optimum trees for all such functions
On the Integrality Gap of a Natural Formulation of the SingleSink Buyatbulk Network Design Problem
, 2001
"... We study two versions of the single sink buyatbulk network design problem. We are given a network and a single sink, and several sources which demand a certain amount of ow to be routed to the sink. ..."
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Cited by 26 (4 self)
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We study two versions of the single sink buyatbulk network design problem. We are given a network and a single sink, and several sources which demand a certain amount of ow to be routed to the sink.
An oblivious o(1)approximation for single source buyatbulk
 Foundations of Computer Science, Annual IEEE Symposium on
, 2009
"... We consider the singlesource (or singlesink) buyatbulk problem with an unknown concave cost function. We want to route a set of demands along a graph to or from a designated root node, and the cost of routing x units of flow along an edge is proportional to some concave, nondecreasing function ..."
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Cited by 7 (1 self)
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for the singlesink buyatbulk problem that proves an O(1) approximation is possible for all f. The number of trees in the support of the distribution constructed by our algorithm is at most 1 + log D.
Approximating BuyatBulk kSteiner trees
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 7 (2006)
, 2006
"... In the buyatbulk kSteiner tree (or rentorbuy kSteiner tree) problem we are given a graph G(V, E) with a set of terminals T ⊆ V including a particular vertex s called the root, and an integer k ≤ T . There are two cost functions on the edges of G, a buy cost b: E − → R + and a rent cost r: E ..."
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− → R +. The goal is to find a subtree H of G rooted at s with at least k terminals so that the cost ∑ b(e) + dist(t, s) is minimize, e∈H t∈T −s where dist(t, s) is the distance from t to s in H with respect to the r cost. Our main result is an O(log 5 n)approximation for the buyatbulk kSteiner tree
Results 1  10
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129,602