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109
Rethinking Virtual Network Embedding: Substrate Support for Path Splitting and Migration
"... Network virtualization is a powerful way to run multiple architectures or experiments simultaneously on a shared infrastructure. However, making efficient use of the underlying resources requires effective techniques for virtual network embedding—mapping each virtual network to specific nodes and li ..."
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Cited by 110 (0 self)
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Network virtualization is a powerful way to run multiple architectures or experiments simultaneously on a shared infrastructure. However, making efficient use of the underlying resources requires effective techniques for virtual network embedding—mapping each virtual network to specific nodes and links in the substrate network. Since the general embedding problem is computationally intractable, past research restricted the problem space to allow efficient solutions, or focused on designing heuristic algorithms. In this paper, we advocate a different approach: rethinking the design of the substrate network to enable simpler embedding algorithms and more efficient use of resources, without restricting the problem space. In particular, we simplify virtual link embedding by: i) allowing the substrate network to split a virtual link over multiple substrate paths and ii) employing path migration to periodically reoptimize the utilization of the substrate network. We also explore nodemapping algorithms that are customized to common classes of virtualnetwork topologies. Our simulation experiments show that path splitting, path migration, and customized embedding algorithms enable a substrate network to satisfy a much larger mix of virtual networks.
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
Primaldual algorithms for connected facility location problems
 Algorithmica
, 2002
"... We consider the Connected Facility Location problem. We are given a graph G = (V, E) with costs {ce} on the edges, a set of facilities F ⊆ V, and a set of clients D ⊆ V. Facility i has a facility opening cost fi and client j has dj units of demand. We are also given a parameter M ≥ 1. A solution ope ..."
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Cited by 76 (7 self)
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We consider the Connected Facility Location problem. We are given a graph G = (V, E) with costs {ce} on the edges, a set of facilities F ⊆ V, and a set of clients D ⊆ V. Facility i has a facility opening cost fi and client j has dj units of demand. We are also given a parameter M ≥ 1. A solution opens some facilities, say F, assigns each client j to an open facility i(j), and connects the open facilities by a Steiner tree T. The total cost incurred is � i∈F fi + � j∈D djci(j)j + M � e∈T ce. We want a solution of minimum cost. A special case of this problem is when all opening costs are 0 and facilities may be opened anywhere, i.e., F = V. If we know a facility v that is open, then the problem becomes a special case of the singlesink buyatbulk problem with two cable types, also known as the rentorbuy problem. We give the first primaldual algorithms for these problems and achieve the best known approximation guarantees. We give a 8.55approximation algorithm for the connected facility location problem and a 4.55approximation algorithm for the rentorbuy problem. Previously the best approximation factors for these problems were 10.66 and 9.001 respectively [8]. Further, these results were not combinatorial — they were obtained by solving an exponential size linear programming relaxation. Our algorithm integrates the primaldual approaches for the facility location problem [11] and the Steiner tree problem [1, 3]. We also consider the connected kmedian problem and give a constantfactor approximation by using our primaldual algorithm for connected facility location. We generalize our results to an edge capacitated variant of these problems and give a constantfactor approximation for these variants.
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
Efficient and robust routing of highly variable traffic
 In Proceedings of Third Workshop on Hot Topics in Networks (HotNetsIII
, 2004
"... ..."
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
Costsharing mechanisms for network design
, 2004
"... We consider a single source network design problem from a gametheoretic perspective. Gupta, Kumar and Roughgarden (Proc. 35th Annual ACM STOC, pages 365372, 2003) developed a simple method for single source rentorbuy problem that also yields the bestknown approximation ratio for the problem. W ..."
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Cited by 33 (5 self)
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We consider a single source network design problem from a gametheoretic perspective. Gupta, Kumar and Roughgarden (Proc. 35th Annual ACM STOC, pages 365372, 2003) developed a simple method for single source rentorbuy problem that also yields the bestknown approximation ratio for the problem. We show how to use a variant of this method to develop an approximately budgetbalanced and group strategyproof costsharing method for the problem. The novelty of our approach stems from our obtaining the costsharing methods for the rentorbuy problem by carefully combining costshares for the simpler problem Steiner tree problem; we feel that this idea may have wider implications. Our algorithm is conceptually simpler than the previous such costsharing method due to P'al and Tardos (Proc. 44th Annual FOCS, pages 584593, 2003), and has a much improved approximation factor of 4:6 (over the previously known factor of 15).
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.
Restoration Algorithms for Virtual Private Networks in the Hose Model
, 2002
"... A Virtual Private Network (VPN) aims to emulate the services provided by a private network over the shared Internet. The endpoints of a VPN are connected using abstractions such as Virtual Channels (VCs) of ATM or Label Switching Paths (LSPs) of MPLS technologies. Reliability of an endtoend VPN co ..."
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Cited by 27 (1 self)
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A Virtual Private Network (VPN) aims to emulate the services provided by a private network over the shared Internet. The endpoints of a VPN are connected using abstractions such as Virtual Channels (VCs) of ATM or Label Switching Paths (LSPs) of MPLS technologies. Reliability of an endtoend VPN connection depends on the reliability of the links and nodes in the fixed path that it traverses in the network. In order to ensure service quality and availability in a VPN, seamless recovery from failures is essential. This work considers the problem of fast recovery in the recently proposed VPN hose model. In the hose model bandwidth is reserved for traffic aggregates instead of pairwise specifications to allow any traffic pattern among the VPN endpoints. This work assumes that the VPN endpoints are connected using a tree structure and at any time, at most one tree link can fail (i.e., single link failure model). A restoration algorithm must select asetofbackup edges and allocate necessary bandwidth on them in advance, so that the traffic disrupted by failure of a primary edge can be rerouted via backup paths. We aim at designing an optimal restoration algorithm to minimize the total bandwidth reserved on the backup edges. This problem is a variant of optimal graph augmentation problem which is NPComplete. Thus, we present a polynomialtime approximation algorithm that guarantees a solution which is at most 16 times of the optimum. The algorithm is based on designing two reductions to convert the original problem to one of adding minimum cost edges to the VPN tree so that the resulting graph is 2connected, which can be solved in polynomial time using known algorithms. The two reductions introduce approximation factors of 8 and 2, respectively, thus resulting in a 16appro...