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45
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 102 (3 self)
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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 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. This problem is motivated by aggregation in sensor networks, as well as by buyatbulk network design.
Simpler and better approximation algorithms for network design
 In Proceedings of the 35th Annual ACM Symposium on Theory of Computing
, 2003
"... We give simple and easytoanalyze randomized approximation algorithms for several wellstudied NPhard network design problems. Our algorithms improve over the previously best known approximation ratios. Our main results are the following. We give a randomized 3.55approximation algorithm for the c ..."
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Cited by 79 (13 self)
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We give simple and easytoanalyze randomized approximation algorithms for several wellstudied NPhard network design problems. Our algorithms improve over the previously best known approximation ratios. Our main results are the following. We give a randomized 3.55approximation algorithm for the connected facility location problem. The algorithm requires three lines to state, one page to analyze, and improves the bestknown performance guarantee for the problem. We give a 5.55approximation algorithm for virtual private network design. Previously, constantfactor approximation algorithms were known only for special cases of this problem. We give a simple constantfactor approximation algorithm for the singlesink buyatbulk network design problem. Our performance guarantee improves over what was previously known, and is an order of magnitude improvement over previous combinatorial approximation algorithms for the problem.
Hardness of BuyatBulk Network Design
, 2004
"... We consider the BuyatBulk network design problem in which we wish to design a network for carrying multicommodity demands from a set of source nodes to a set of destination nodes. The key feature of the problem is that the cost of capacity on each edge is concave and hence exhibits economies of sc ..."
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Cited by 59 (4 self)
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We consider the BuyatBulk network design problem in which we wish to design a network for carrying multicommodity demands from a set of source nodes to a set of destination nodes. The key feature of the problem is that the cost of capacity on each edge is concave and hence exhibits economies of scale. If the cost of capacity per unit length can be different on different edges then we say that the problem is nonuniform. The problem is uniform otherwise.
A constant factor approximation for the single sink edge installation problems
 In Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing (STOC
, 2001
"... We present the first constant approximation to the single sink buyatbulk network design problem, where we have to design a network by buying pipes of different costs and capacities per unit length to route demands at a set of sources to a single sink. The distances in the underlying network form a ..."
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Cited by 59 (1 self)
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We present the first constant approximation to the single sink buyatbulk network design problem, where we have to design a network by buying pipes of different costs and capacities per unit length to route demands at a set of sources to a single sink. The distances in the underlying network form a metric. This result improves the previous bound of O(log R), where R is the set of sources. We also present a better constant approximation to the related Access Network Design problem. Our algorithms are randomized and combinatorial. As a subroutine in our algorithm, we use an interesting variant of facility location with lower bounds on the amount of demand an open facility needs to serve. We call this variant load balanced facility location, and present a constant factor approximation for it, while relaxing the lower bounds by a constant factor.
Approximation algorithms for nonuniform buyatbulk network design problems
 Proc. of IEEE FOCS
"... Abstract. Buyatbulk network design problems arise in settings where the costs for purchasing or installing equipment exhibit economies of scale. The objective is to build a network of cheapest cost to support a given multicommodity flow demand between node pairs. We present approximation algorith ..."
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Cited by 53 (15 self)
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Abstract. Buyatbulk network design problems arise in settings where the costs for purchasing or installing equipment exhibit economies of scale. The objective is to build a network of cheapest cost to support a given multicommodity flow demand between node pairs. We present approximation algorithms for buyatbulk network design problems with costs on both edges and nodes of an undirected graph. Our main result is the first polylogarithmic approximation ratio for the nonuniform problem that allows different cost functions on each edge and node; the ratio we achieve is O(log4 h) where h is the number of demand pairs. In addition we present an O(log h) approximation for the single sink problem. Polylogarithmic ratios for some related problems are also obtained. Our algorithm for the multicommodity problem is obtained via a reduction to the single source problem using the notion of junction trees. We believe that this presents a simple yet useful general technique for network design problems. Key words. Nonuniform buyatbulk, network design, approximation algorithm, concave cost, network flow, economies of scale AMS subject classifications. 68Q25, 68W25, 90C27, 90C59 1. Introduction. Network
Approximation via costsharing: a simple approximation algorithm for the multicommodity rentorbuy problem
 In IEEE Symposium on Foundations of Computer Science (FOCS
, 2003
"... We study the multicommodity rentorbuy problem, a type of network design problem with economies of scale. In this problem, capacity on an edge can be rented, with cost incurred on a perunit of capacity basis, or bought, which allows unlimited use after payment of a large fixed cost. Given a graph ..."
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Cited by 46 (7 self)
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We study the multicommodity rentorbuy problem, a type of network design problem with economies of scale. In this problem, capacity on an edge can be rented, with cost incurred on a perunit of capacity basis, or bought, which allows unlimited use after payment of a large fixed cost. Given a graph and a set of sourcesink pairs, we seek a minimumcost way of installing sufficient capacity on edges so that a prescribed amount of flow can be sent simultaneously from each source to the corresponding sink. The first constantfactor approximation algorithm for this problem was recently given by Kumar et al. (FOCS ’02); however, this algorithm and its analysis are both quite complicated, and its performance guarantee is extremely large. In this paper, we give a conceptually simple 12approximation algorithm for this problem. Our analysis of this algorithm makes crucial use of cost sharing, the task of allocating the cost of an object to many users of the object in a “fair ” manner. While techniques from approximation algorithms have recently yielded new progress on cost sharing problems, our work is the first to show the converse— that ideas from cost sharing can be fruitfully applied in the design and analysis of approximation algorithms. 1
Opus: an Overlay Peer Utility Service
 In Proceedings of the 5th International Conference on Open Architectures and Network Programming (OPENARCH
, 2002
"... Today, an increasing number of important network services, such as content distribution, replicated services, and storage systems, are deploying overlays across multiple Internet sites to deliver better performance, reliability and adaptability. Currently however, such network services must indi ..."
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Cited by 41 (9 self)
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Today, an increasing number of important network services, such as content distribution, replicated services, and storage systems, are deploying overlays across multiple Internet sites to deliver better performance, reliability and adaptability. Currently however, such network services must individually reimplement substantially similar functionality. For example, applications must configure the overlay to meet their specific demands for scale, service quality and reliability. Further, they must dynamically map data and functions onto network resourcesincluding servers, storage, and network pathsto adapt to changes in load or network conditions.
A deterministic algorithm for the costdistance problem
 In Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms
, 2001
"... The COSTDISTANCE network design problem is the following. We are given an undirected graph, a designated root vertex, and a set of terminals. We are also given two nonnegative real valued functions defined on, namely, a cost function and a length function, and a nonnegative weight function on the ..."
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Cited by 34 (0 self)
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The COSTDISTANCE network design problem is the following. We are given an undirected graph, a designated root vertex, and a set of terminals. We are also given two nonnegative real valued functions defined on, namely, a cost function and a length function, and a nonnegative weight function on the set. The goal is to find a tree that connects the terminals in to the root and minimizes!"$ # , where is the length of the path in from + to. We give a deterministic. 2435,/10 approximation algorithm for the COSTDISTANCE network design problem, in a sense derandomizing the algorithm given in [4]. Our algorithm is based on a natural 6/70)2835 linear programming relaxation of the problem and in the process we show that its integrality. gap is. Introduction: We study the COSTDISTANCE network design problem, recently defined by Meyerson,
Oblivious network design
 In Proceedings of the 17th Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2006
"... Consider the following network design problem: given a network G = (V, E), sourcesink pairs {si, ti} arrive and desire to send a unit of flow between themselves. The cost of the routing is this: if edge e carries a total of fe flow (from all the terminal pairs), the cost is given by ∑ e ℓ(fe), wher ..."
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Cited by 32 (8 self)
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Consider the following network design problem: given a network G = (V, E), sourcesink pairs {si, ti} arrive and desire to send a unit of flow between themselves. The cost of the routing is this: if edge e carries a total of fe flow (from all the terminal pairs), the cost is given by ∑ e ℓ(fe), where ℓ is some concave cost function; the goal is to minimize the total cost incurred. However, we want the routing to be oblivious: when terminal pair {si, ti} makes its routing decisions, it does not know the current flow on the edges of the network, nor the identity of the other pairs in the system. Moreover, it does not even know the identity of the function ℓ, merely knowing that ℓ is a concave function of the total flow on the edge. How should it (obliviously) route its one unit of flow?