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52
Tight approximation algorithms for maximum general assignment problems
 Proc. of ACMSIAM SODA
, 2006
"... A separable assignment problem (SAP) is defined by a set of bins and a set of items to pack in each bin; a value, fij, for assigning item j to bin i; and a separate packing constraint for each bin – i.e. for bin i, a family Ii of subsets of items that fit in bin i. The goal is to pack items into bin ..."
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Cited by 42 (7 self)
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A separable assignment problem (SAP) is defined by a set of bins and a set of items to pack in each bin; a value, fij, for assigning item j to bin i; and a separate packing constraint for each bin – i.e. for bin i, a family Ii of subsets of items that fit in bin i. The goal is to pack items into bins to maximize the aggregate value. This class of problems includes the maximum generalized assignment problem (GAP) 1) and a distributed caching problem (DCP) described in this paper. Given a βapproximation algorithm for finding the highest value packing of a single bin, we give 1. A polynomialtime LProunding based ((1 − 1 e)β)approximation algorithm. 2. A simple polynomialtime local search ( β approximation algorithm, for any ɛ> 0. β+1 − ɛ)Therefore, for all examples of SAP that admit an approximation scheme for the singlebin problem, we obtain an LPbased algorithm with (1 − 1 e − ɛ)approximation and a local search algorithm with ( 1 2 −ɛ)approximation guarantee. Furthermore, for cases in which the subproblem admits a fully polynomial approximation scheme (such as for GAP), the LPbased algorithm analysis can be strengthened to give a guarantee of 1 − 1 e. The best previously known approximation algorithm for GAP is a 1 2approximation by Shmoys and Tardos; and Chekuri and Khanna. Our LP algorithm is based on rounding a new linear programming relaxation, with a provably better integrality gap. To complement these results, we show that SAP and DCP cannot be approximated within a factor better than 1 − 1 e unless NP ⊆ DTIME(n O(log log n)), even if there exists a polynomialtime exact algorithm for the singlebin problem.
A Framework for Evaluating Replica Placement Algorithms
, 2002
"... This paper introduces a framework for evaluating replica placement algorithms (RPA) for content delivery networks (CDN) as well as RPAs from other fields that might be applicable to current or future CDNs. First, the framework classifies and qualitatively compares RPAs using a generic set of primiti ..."
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Cited by 37 (1 self)
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This paper introduces a framework for evaluating replica placement algorithms (RPA) for content delivery networks (CDN) as well as RPAs from other fields that might be applicable to current or future CDNs. First, the framework classifies and qualitatively compares RPAs using a generic set of primitives that capture problem definitions and heuristics. Second, it provides estimates for the decision times of RPAs using an analytic model. To achieve accuracy, the model takes into account disk accesses and message sizes, in addition to computational complexity and message numbers that have been considered traditionally. Third, it uses the "goodness" of produced placements to compare RPAs even when they have different problem definitions. Based on these evaluations, we identify open issues and potential areas for future research.
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 27 (3 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.
Distributed Selfstabilizing Placement of Replicated Resources in Emerging Networks
 IEEE/ACM Trans. Netw
, 2005
"... Emerging large scale distributed networking systems, such as P2P file sharing systems, sensor networks, and ad hoc wireless networks, require replication of content, functionality, or configuration to enact or optimize communication tasks. The placement of these replicated resources can significantl ..."
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Cited by 19 (2 self)
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Emerging large scale distributed networking systems, such as P2P file sharing systems, sensor networks, and ad hoc wireless networks, require replication of content, functionality, or configuration to enact or optimize communication tasks. The placement of these replicated resources can significantly impact performance. We present a novel selfstabilizing, fully distributed, asynchronous, scalable protocol that can be used to place replicated resources such that each node is “close ” to some copy of any object. We describe our protocol in the context of a graph with colored nodes, where a node’s color indicates the replica/task that it is assigned. Our combination of theoretical results and simulation prove stabilization of the protocol, and evaluate its performance in the context of convergence time, message transmissions, and color distance. Our results show that the protocol generates colorings that are close to the optimal under a set of metrics, making such a protocol ideal for emerging networking systems. 1
Optimal Content Placement for a Largescale VoD System
 In ACM CoNEXT
, 2010
"... IPTV service providers offering VideoonDemand currently use servers at each metropolitan office to store all the videos in their library. With the rapid increase in library sizes, it will soon become infeasible to replicate the entire library at each office. We present an approach for intelligent ..."
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Cited by 18 (2 self)
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IPTV service providers offering VideoonDemand currently use servers at each metropolitan office to store all the videos in their library. With the rapid increase in library sizes, it will soon become infeasible to replicate the entire library at each office. We present an approach for intelligent content placement that scales to large library sizes (e.g., 100Ks of videos). We formulate the problem as a mixed integer program (MIP) that takes into account constraints such as disk space, link bandwidth, and content popularity. To overcome the challenges of scale, we employ a Lagrangian relaxationbased decomposition technique combined with integer rounding. Our technique finds a nearoptimal solution (e.g., within 12%) with orders of magnitude speedup relative to solving even the LP relaxation via standard software. We also present simple strategies to address practical issues such as popularity estimation, content updates, shortterm popularity fluctuation, and frequency of placement updates. Using traces from an operational system, we show that our approach significantly outperforms simpler placement strategies. For instance, our MIPbased solution can serve all requests using only half the link bandwidth used by LRU or LFU cache replacement policies. We also investigate the tradeoff between disk space and network bandwidth. 1.
Designing overlay multicast networks for streaming
 In Proceedings of ACM Symposium on Parallel Algorithms and Architectures
, 2003
"... In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within a logarithmic factor. The class of networks that ..."
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Cited by 16 (4 self)
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In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within a logarithmic factor. The class of networks that our algorithm applies to includes the one used by Akamai Technologies to deliver live media streams over the Internet. In particular, we analyze networks consisting of three stages of nodes. The nodes in the first stage are the sources where live streams originate. A source forwards each of its streams to one or more nodes in the second stage, which are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage, which are called the sinks. As the packets in a stream travel from one stage to the next, some of them may be lost. The job of a sink is to combine the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. We assume that the loss rate between any pair of nodes in the network is known, and that losses between different pairs are independent, but discuss extensions in which some losses may be correlated.
Approximation Algorithms for Data Management in Networks
, 2001
"... This paper deals with static data management in computer systems connected by networks. A basic functionality in these systems is the interactive ..."
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Cited by 15 (0 self)
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This paper deals with static data management in computer systems connected by networks. A basic functionality in these systems is the interactive
Facility location with service installation costs
 In Proceedings of the 15th Annual ACMSIAM Symposium on Discrete Algorithms
, 2004
"... Our main result is a primaldual 6approximation algorithm under the assumption that there is an ordering on the facilities such that if i comes before i0 in this ordering then for every service type l, fli < = fli0. This includes (as special cases) the settings where the service installation cost f ..."
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Cited by 14 (6 self)
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Our main result is a primaldual 6approximation algorithm under the assumption that there is an ordering on the facilities such that if i comes before i0 in this ordering then for every service type l, fli < = fli0. This includes (as special cases) the settings where the service installation cost fli depends only on the service type l, or depends only on the location i. With arbitrary service installation costs, the problem becomes as hard as the setcover problem. Our algorithm extends the algorithm of Jain & Vazirani [9] in a novel way. If the service installation cost depends only on the service type and not on the location, we give an LP rounding algorithm that attains an improved approximation ratio of 2.391. The algorithm combines both clustered randomized rounding [6] and the filtering based technique of [10, 14]. We also consider the kmedian version of the problem where there is an additional requirement that at most k facilities may be opened. We use our primaldual algorithm to give a constantfactor approximation for this problem when the service installation cost depends only on the service type. 1 Introduction Facility location problems have been widely studied inthe Operations Research community (see for e.g. [12]). In its simplest version, uncapacitated facility location(UFL), we are given a set of facilities, F, and a set of demands or clients D. Each facility i has a facilityopening cost
Approximation Algorithms for Clustering Problems
, 2004
"... Clustering is a ubiquitous problem that arises in many applications in different fields such as data mining, image processing, machine learning, and bioinformatics. Clustering problems have been extensively studied as optimization problems with various objective functions in the Operations Research ..."
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Cited by 14 (5 self)
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Clustering is a ubiquitous problem that arises in many applications in different fields such as data mining, image processing, machine learning, and bioinformatics. Clustering problems have been extensively studied as optimization problems with various objective functions in the Operations Research and Computer Science literature. We focus on a class of objective functions more commonly referred to as facility location problems. These problems arise in a wide range of applications such as, plant or warehouse location problems, cache placement problems, and network design problems where the costs obey economies of scale. In the simplest of these problems, the uncapacitated facility location (UFL) problem, we want to open facilities at some subset of a given set of locations and assign each client in a given set D to an open facility so as to minimize the sum of the facility opening costs and client assignment costs. This is a very wellstudied problem; however it fails to address many of the requirements of real applications. In this thesis we consider various problems that build upon UFL and capture additional issues that arise in applications such as, uncertainties in the data, clients with different service needs, and facilities with interconnectivity requirements. By focusing initially on facility location problems in these new models, we develop new algorithmic techniques that will find application in a wide range of settings. We consider a widely used paradigm in stochastic programming to model settings where the underlying data, for example, the locations or demands of the clients, may be uncertain: the 2stage with recourse model that involves making some initial decisions, observing additional information, and then augmenting the initial decisions, if necessary, by taking recourse actions. We present a randomized polynomial time
Content and Service Replication Strategies in Multihop Wireless Mesh Networks
 In MSWiM
, 2005
"... Emerging multihop wireless mesh networks have much different characteristics than the Internet. They have low dimensionality and large diameters. Content and service replication can greatly improve their scalability. However, replication strategies in such networks have not been well studied. This ..."
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Cited by 13 (1 self)
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Emerging multihop wireless mesh networks have much different characteristics than the Internet. They have low dimensionality and large diameters. Content and service replication can greatly improve their scalability. However, replication strategies in such networks have not been well studied. This paper studies the optimality of replication strategies and explores it in multihop wireless mesh networks for the first time. We start with the problem of determining the optimal numbers of replicas for a set of objects which have distinct probabilities of being requested in large 2D mesh networks. We reveal the structure of the optimal replication strategy to minimize object access cost. To minimize average cost to access an object in 2D mesh networks, the optimal strategy replicates an object such that the number of its replicas is proportional , where p is the access probability of the object. This result indicates the inefficiency of demanddriven content and service replication in 2D mesh networks, where an object is replicated such that the number of its replicas is proportional to p. We further study practical, online algorithms to approximate the optimal strategy. Interestingly, the optimal replication can be approximated well by a localized replacement algorithm. The algorithm utilizes only handy information and incurs no communication overhead. The paper demonstrates a significant performance gain by the optimal strategy, and the effectiveness of the online replacement algorithm.