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18
Maximizing the Spread of Influence Through a Social Network
 In KDD
, 2003
"... Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in gametheoretic settings, and the effects of ..."
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Cited by 963 (6 self)
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Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in gametheoretic settings, and the effects of “word of mouth ” in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target? We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NPhard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63 % of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks. We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly outperform nodeselection heuristics based on the wellstudied notions of degree centrality and distance centrality from the field of social networks.
Segmentation problems
, 2004
"... We study a novel genre of optimization problems, which we call segmentation problems, motivated in part by certain aspects of clustering and data mining. For any classical optimization problem, the corresponding segmentation problem seeks to partition a set of cost vectors into several segments, s ..."
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Cited by 86 (5 self)
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We study a novel genre of optimization problems, which we call segmentation problems, motivated in part by certain aspects of clustering and data mining. For any classical optimization problem, the corresponding segmentation problem seeks to partition a set of cost vectors into several segments, so that the overall cost is optimized. We focus on two natural and interesting (but MAXSNPcomplete) problems in this class, the HYPERCUBE SEGMENTATION PROBLEM and the CATALOG SEGMENTATION PROBLEM, and present approximation algorithms for them. We also present a general greedy scheme, which can be specialized to approximate any segmentation problem.
Approximating the Throughput of Multiple Machines in RealTime Scheduling
"... We consider the following fundamental scheduling problem. The input to the problem consists of n jobs and k machines. Each of the jobs is associated with a release time, a deadline, a weight, and a processing time on each of the machines. The goal is to find a schedule that maximizes the weight of j ..."
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Cited by 76 (7 self)
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We consider the following fundamental scheduling problem. The input to the problem consists of n jobs and k machines. Each of the jobs is associated with a release time, a deadline, a weight, and a processing time on each of the machines. The goal is to find a schedule that maximizes the weight of jobs that meet their deadline. We give constant factor approximation algorithms for four variants of the problem, depending on the type of the machines (identical vs. unrelated), and the weight of the jobs (identical vs. arbitrary). All these variants are known to be NPHard, and we observe that the two variants involving unrelated machines are also MAXSNP hard. To the best of our knowledge, these are the first approximation algorithms for such problems in the nonpreemptive o line setting. The specific results obtained are:  For identical job weights and unrelated machines: a greedy 2approximation algorithm.  For identical job weights and k identical machines: the same greedy alg...
Algorithms for Subset Selection in Linear Regression
 STOC'08
, 2008
"... We study the problem of selecting a subset of k random variables to observe that will yield the best linear prediction of another variable of interest, given the pairwise correlations between the observation variables and the predictor variable. Under approximation preserving reductions, this proble ..."
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Cited by 55 (3 self)
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We study the problem of selecting a subset of k random variables to observe that will yield the best linear prediction of another variable of interest, given the pairwise correlations between the observation variables and the predictor variable. Under approximation preserving reductions, this problem is also equivalent to the“sparse approximation”problem of approximating signals concisely. We propose and analyze exact and approximation algorithms for several special cases of practical interest. We give an FPTAS when the covariance matrix has constant bandwidth, and exact algorithms when the associated covariance graph, consisting of edges for pairs of variables with nonzero correlation, forms a tree or has a large (known) independent set. Furthermore, we give an exact algorithm when the variables can be embedded into a line such that the covariance decreases exponentially in the distance, and a constantfactor approximation when the variables have no “conditional suppressor variables”. Much of our reasoning is based on perturbation results for the R 2 multiple correlation measure, frequently used as a measure for “goodnessoffit statistics”. It lies at the core of our FPTAS, and also allows us to extend exact algorithms to approximation algorithms when the matrix “nearly ” falls into one of the above classes. We also use perturbation analysis to prove approximation guarantees for the widely used “Forward Regression ” heuristic when the observation variables are nearly independent.
Survivable networks, linear programming relaxations and the parsimonious property
, 1993
"... We consider the survivable network design problem the problem of designing, at minimum cost, a network with edgeconnectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the kedgeconnected network design problem. We establ ..."
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Cited by 54 (11 self)
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We consider the survivable network design problem the problem of designing, at minimum cost, a network with edgeconnectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the kedgeconnected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic improvements and we perform tight worstcase analyses of two heuristics for the survivable network design problem.
Online Competitive Algorithms for Call Admission in Optical Networks
, 1996
"... We study the online call admission problem in optical networks. We present a general technique that allows us to reduce the problem of call admission and wavelength selection to the call admission problem. We then give randomized algorithms with logarithmic competitive ratios for specific topolo ..."
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Cited by 47 (6 self)
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We study the online call admission problem in optical networks. We present a general technique that allows us to reduce the problem of call admission and wavelength selection to the call admission problem. We then give randomized algorithms with logarithmic competitive ratios for specific topologies in switchless and reconfigurable optical networks. We conclude by considering full duplex communications.
OnLine Randomized Call Control Revisited
 SIAM J. COMPUTING
, 2001
"... We consider the problem of online call admission and routing on trees and meshes. Previous work gave randomized online algorithms for these problems and proved that they have optimal (up to constant factors) competitive ratios. However, these algorithms can obtain very low profit with high probabi ..."
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Cited by 29 (5 self)
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We consider the problem of online call admission and routing on trees and meshes. Previous work gave randomized online algorithms for these problems and proved that they have optimal (up to constant factors) competitive ratios. However, these algorithms can obtain very low profit with high probability. We investigate the question of devising for these problems online competitive algorithms that also guarantee a "good" solution with "good" probability. We give a new
Stochastic Submodular Maximization
"... We study stochastic submodular maximization problem with respect to a cardinality constraint. Our model can capture the effect of uncertainty in different problems, such as cascade effects in social networks, capital budgeting, sensor placement, etc. We study nonadaptive and adaptive policies and ..."
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Cited by 15 (1 self)
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We study stochastic submodular maximization problem with respect to a cardinality constraint. Our model can capture the effect of uncertainty in different problems, such as cascade effects in social networks, capital budgeting, sensor placement, etc. We study nonadaptive and adaptive policies and give optimal constant approximation algorithms for both cases. We also bound the adaptivity gap of the problem between 1.21 and 1.59.
Minimizing Request Blocking in AllOptical Rings
 In Proc. INFOCOM 2003
, 2003
"... In alloptical networks that use WDM technology it is often the case that several communication requests have to be blocked, due to bandwidth and technology limitations. Minimizing request blocking is therefore an important task calling for algorithmic techniques for efficient routing and wavelength ..."
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Cited by 12 (4 self)
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In alloptical networks that use WDM technology it is often the case that several communication requests have to be blocked, due to bandwidth and technology limitations. Minimizing request blocking is therefore an important task calling for algorithmic techniques for efficient routing and wavelength assignment.