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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 990 (7 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.
Approximation algorithms for metric facility location and kmedian problems using the . . .
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Branchandprice: Column generation for solving huge integer programs
 OPER. RES
, 1998
"... We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchandbound tree. We present classes of models for which t ..."
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Cited by 360 (13 self)
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We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchandbound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. We then discuss computational issues and implementation of column generation, branchandbound algorithms, including special branching rules and efficient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality.
Metaheuristics in combinatorial optimization: Overview and conceptual comparison
 ACM COMPUTING SURVEYS
, 2003
"... The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important meta ..."
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Cited by 314 (17 self)
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The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.
A Fast LinearArithmetic Solver for DPLL(T)
, 2006
"... We present a new Simplexbased linear arithmetic solver that can be integrated efficiently in the DPLL(T) framework. The new solver improves over existing approaches by enabling fast backtracking, supporting a priori simplification to reduce the problem size, and providing an efficient form of the ..."
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Cited by 289 (13 self)
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We present a new Simplexbased linear arithmetic solver that can be integrated efficiently in the DPLL(T) framework. The new solver improves over existing approaches by enabling fast backtracking, supporting a priori simplification to reduce the problem size, and providing an efficient form of theory propagation. We also present a new and simple approach for solving strict inequalities. Experimental results show substantial performance improvements over existing tools that use other Simplexbased solvers in DPLL(T) decision procedures. The new solver is even competitive with stateoftheart tools specialized for the difference logic fragment.
Robust discrete optimization and network flows
 Mathematical Programming Series B
, 2003
"... We propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. In particular, when both the cost coefficients and the data ..."
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Cited by 194 (27 self)
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We propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. In particular, when both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we propose a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation. When only the cost coefficients are subject to uncertainty and the problem is a 0 − 1 discrete optimization problem on n variables, then we solve the robust counterpart by solving at most n+1 instances of the original problem. Thus, the robust counterpart of a polynomially solvable 0−1 discrete optimization problem remains polynomially solvable. In particular, robust matching, spanning tree, shortest path, matroid intersection, etc. are polynomially solvable. We also show that the robust counterpart of an NPhard αapproximable 0 − 1 discrete optimization problem, remains αapproximable. Finally, we propose an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network.
A Survey of Computational Complexity Results in Systems and Control
, 2000
"... The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fi ..."
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Cited by 187 (18 self)
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The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial time algorithms, NPcompleteness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, timevarying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
MinimumCost Multicast over Coded Packet Networks
 IEEE TRANS. ON INF. THE
, 2006
"... We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as b ..."
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Cited by 164 (28 self)
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We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomialtime solvable optimization problem, ... and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimumcost multicast. By contrast, establishing minimumcost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.