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76
Approximation Algorithms for Data Placement in Arbitrary Networks
, 2001
"... We study approximation algorithms for placing replicated data in arbitrary networks. Consider a network of nodes with individual storage capacities and a metric communication cost function, in which each node periodically issues a request for an object drawn from a collection of uniformlength objec ..."
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Cited by 84 (4 self)
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We study approximation algorithms for placing replicated data in arbitrary networks. Consider a network of nodes with individual storage capacities and a metric communication cost function, in which each node periodically issues a request for an object drawn from a collection of uniformlength objects. We consider the problem of placing copies of the objects among the nodes such that the average access cost is minimized. Our main result is a polynomialtime constantfactor approximation algorithm for this placement problem. Our algorithm is based on a careful rounding of a linear programming relaxation of the problem. We also show that the data placement problem is MAXSNPhard. We extend our approximation result to a generalization of the data placement problem that models additional costs such as the cost of realizing the placement. We also show that when object lengths are nonuniform, a constantfactor approximation is achievable if the capacity at each node in the approximate solution is allowed to exceed that in the optimal solution by the length of the largest object.
Hedging uncertainty: Approximation algorithms for stochastic optimization problems
 In Proceedings of the 10th International Conference on Integer Programming and Combinatorial Optimization
, 2004
"... We initiate the design of approximation algorithms for stochastic combinatorial optimization problems; we formulate the problems in the framework of twostage stochastic optimization, and provide nearly tight approximation algorithms. Our problems range from the simple (shortest path, vertex cover, ..."
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Cited by 77 (13 self)
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We initiate the design of approximation algorithms for stochastic combinatorial optimization problems; we formulate the problems in the framework of twostage stochastic optimization, and provide nearly tight approximation algorithms. Our problems range from the simple (shortest path, vertex cover, bin packing) to complex (facility location, set cover), and contain representatives with different approximation ratios. The approximation ratio of the stochastic variant of a typical problem is of the same order of magnitude as its deterministic counterpart. Furthermore, common techniques for designing approximation algorithms such as LP rounding, the primaldual method, and the greedy algorithm, can be carefully adapted to obtain these results. 1
An Improved LPbased Approximation for Steiner Tree
, 2009
"... The Steiner tree problem is one of the most fundamentalhard problems: given a weighted undirected graph and a subset of terminal nodes, find a minimum weight tree spanning the terminals. In a sequence of papers, the approximation ratio for this problem was improved from to the current best���[Robin ..."
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Cited by 65 (7 self)
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The Steiner tree problem is one of the most fundamentalhard problems: given a weighted undirected graph and a subset of terminal nodes, find a minimum weight tree spanning the terminals. In a sequence of papers, the approximation ratio for this problem was improved from to the current best���[Robins,ZelikovskySIDMA’05]. All these algorithms are purely combinatorial. A longstanding open problem is whether there is an LPrelaxation for Steiner tree with integrality gap smaller than [Vazirani,RajagopalanSODA’99]. In this paper we improve the approximation factor for Steiner tree, developing an LPbased approximation a� algorithm. Our algorithm is based on a, seemingly novel, iterative randomized rounding technique. We consider a directedcomponent cut relaxation for the�restricted Steiner tree problem. We sample one of these components with probability proportional to the value of the associated variable in the optimal fractional solution and contract it. We iterate this process for a proper number of times and finally output the sampled components together
Benefitbased data caching in ad hoc networks
 In Proceedings of the 2006 14th IEEE International Conference on Network Protocols ICNP ’06
, 2006
"... Abstract — Data caching can significantly improve the efficiency of information access in a wireless ad hoc network by reducing the access latency and bandwidth usage. However, designing efficient distributed caching algorithms is nontrivial when network nodes have limited memory. In this article, ..."
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Cited by 50 (4 self)
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Abstract — Data caching can significantly improve the efficiency of information access in a wireless ad hoc network by reducing the access latency and bandwidth usage. However, designing efficient distributed caching algorithms is nontrivial when network nodes have limited memory. In this article, we consider the cache placement problem of minimizing total data access cost in ad hoc networks with multiple data items and nodes with limited memory capacity. The above optimization problem is known to be NPhard. Defining benefit as the reduction in total access cost, we present a polynomialtime centralized approximation algorithm that provably delivers a solution whose benefit is at least onefourth (onehalf for uniformsize data items) of the optimal benefit. The approximation algorithm is amenable to localized distributed implementation, which is shown via simulations to perform close to the approximation algorithm. Our distributed algorithm naturally extends to networks with mobile nodes. We simulate our distributed algorithm using a network simulator (ns2), and demonstrate that it significantly outperforms another existing caching technique (by Yin and Cao [31]) in all important performance metrics. The performance differential is particularly large in more challenging scenarios, such as higher access frequency and smaller memory. Index Terms caching placement policy, ad hoc networks, algorithm/protocol design and analysis, simulations. I.
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
Bidimensionality: New Connections between FPT Algorithms and PTASs
, 2005
"... We demonstrate a new connection between fixedparametertractability and approximation algorithms for combinatorial optimization problems on planar graphs and their generalizations. Specifically, we extend the theory of socalled "bidimensional " problems to show that essentially ..."
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Cited by 43 (7 self)
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We demonstrate a new connection between fixedparametertractability and approximation algorithms for combinatorial optimization problems on planar graphs and their generalizations. Specifically, we extend the theory of socalled &quot;bidimensional &quot; problems to show that essentially all such problems have both subexponential fixedparameter algorithms and PTASs. Bidimensional problems include e.g. feedbackvertex set, vertex cover, minimum maximal matching, face cover, a series of vertexremoval problems, dominating set,edge dominating set,
Optimal Bandwidth Reservation in HoseModel VPNs with MultiPath Routing
 IEEE Infocom
, 2004
"... A virtual private network (VPN) provides private network connections over a publicly accessible shared network. Bandwidth provisioning for VPNs leads to challenging optimization problems. In the hose model proposed by Duffield et al., each VPN endpoint specifies bounds on the total amount of traffic ..."
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Cited by 33 (0 self)
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A virtual private network (VPN) provides private network connections over a publicly accessible shared network. Bandwidth provisioning for VPNs leads to challenging optimization problems. In the hose model proposed by Duffield et al., each VPN endpoint specifies bounds on the total amount of traffic that it will send or receive at any time. The network provider must provision the VPN so that there is sufficient bandwidth for any traffic matrix that is consistent with these bounds. While previous work has considered tree routing and singlepath routing between the VPN endpoints, we demonstrate that the use of multipath routing offers significant advantages. On the one hand, we present an optimal polynomialtime algorithm that computes a bandwidth reservation of minimum cost using multipath routing. This is in contrast to tree routing and singlepath routing, where the problem is computationally hard. On the other hand, we present experimental results showing that the reservation cost using multipath routing can indeed be significantly smaller than with tree or singlepath routing.
Fixedparameter algorithms for the (k, r)center in planar graphs and map graphs
 ACM TRANSACTIONS ON ALGORITHMS
, 2003
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On the Approximability of Some Network Design Problems
, 2005
"... Consider the following classical network design problem: aset of terminals T = ftig wants to send traffic to a "root" r in an nnode graph G = (V; E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocatedon the edges to permit this. However, bandwidth on an ..."
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Cited by 30 (3 self)
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Consider the following classical network design problem: aset of terminals T = ftig wants to send traffic to a "root" r in an nnode graph G = (V; E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocatedon the edges to permit this. However, bandwidth on an edge e can only be allocated in integral multiples of some basecapacity ue and hence provisioning k \Theta ue bandwidth onedge e incurs a cost of dke times the cost of that edge. Theobjective is a minimumcost feasible solution. This is one of many network design problems widelystudied where the bandwidth allocation being governed by side constraints: edges may only allow a subset of cables tobe purchased on them, or certain qualityofservice requirements may have to be met.In this work, we show that the above problem, and in fact, several basic problems in this general network designframework, cannot be approximated better than \Omega (log log n)unless NP ` DTIME \Gamma nO(log log log n) \Delta. In particular,
Approximation via Cost Sharing: Simpler and better approximation algorithms for network design
, 2005
"... We present constantfactor approximation algorithms for several widelystudied NPhard optimization problems in network design, including the multicommodity rentorbuy, virtual private network design, and singlesink buyatbulk problems. Our algorithms are simple and their approximation ratios imp ..."
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Cited by 26 (3 self)
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We present constantfactor approximation algorithms for several widelystudied NPhard optimization problems in network design, including the multicommodity rentorbuy, virtual private network design, and singlesink buyatbulk problems. Our algorithms are simple and their approximation ratios improve over those previously known, in some cases by orders of magnitude. We develop a general analysis framework to bound the approximation ratios of our algorithms. This framework is based on a novel connection between random sampling and gametheoretic cost sharing. While techniques from approximation algorithms have recently yielded new progress on costsharing problems, our work is the first to show the conversethat ideas from cost sharing can be fruitfully applied in the design and analysis of approximation algorithms.