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Approximability of Adaptive Seeding under Knapsack Constraints
, 2015
"... Adapting Seeding is a key algorithmic challenge of influence maximization in social networks. One seeks to select among certain available nodes in a network, and then, adaptively, among neighbors of those nodes as they become available, in order to maximize influence in the overall network. Despite ..."
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Adapting Seeding is a key algorithmic challenge of influence maximization in social networks. One seeks to select among certain available nodes in a network, and then, adaptively, among neighbors of those nodes as they become available, in order to maximize influence in the overall network. Despite recent strong approximation results [25, 1], very little is known about the problem when nodes can take on different activation costs. Surprisingly, designing adaptive seeding algorithms that can appropriately incentivize users with heterogeneous activation costs introduces fundamental challenges that do not exist in the simplified version of the problem. In this paper we study the approximability of adaptive seeding algorithms that incentivize nodes with heterogeneous activation costs. We first show a tight inapproximability result which applies even for a very restricted version of the problem. We then complement this inapproximability with a constantfactor approximation for general submodular functions, showing that the difficulties caused by the stochastic nature of the problem can be overcome. In addition, we show stronger approximation results for additive influence functions and cases where the nodes’ activation costs constitute a small fraction of the budget.
Streaming Algorithms for Submodular Function Maximization
, 2015
"... We consider the problem of maximizing a nonnegative submodular set function f: 2N → R+ subject to a pmatchoid constraint in the singlepass streaming setting. Previous work in this context has considered streaming algorithms for modular functions and monotone submodular functions. The main result i ..."
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We consider the problem of maximizing a nonnegative submodular set function f: 2N → R+ subject to a pmatchoid constraint in the singlepass streaming setting. Previous work in this context has considered streaming algorithms for modular functions and monotone submodular functions. The main result is for submodular functions that are nonmonotone. We describe deterministic and randomized algorithms that obtain a Ω(1p)approximation using O(k log k)space, where k is an upper bound on the cardinality of the desired set. The model assumes value oracle access to f and membership oracles for the matroids defining the pmatchoid constraint.
Research Statement
"... My research interest is in the design and analysis of algorithms for optimization. I am strongly motivated by applications, particularly in machine learning and the design of electronic markets. As a theoretician, I believe in formulating problems that are fundamental to these applications and yet s ..."
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My research interest is in the design and analysis of algorithms for optimization. I am strongly motivated by applications, particularly in machine learning and the design of electronic markets. As a theoretician, I believe in formulating problems that are fundamental to these applications and yet sufficiently general to be applicable to a wide variety of domains. This has led me to focus on two areas, sequential decision making and discrete nonlinear optimization, introducing broad new problem formulations and solving them by novel algorithmic techniques. We are surrounded by problems where we need to make decisions without having some or all of the relevant information. However, we can learn from the results of our past actions. Examples of such problems are learning clickthrough rates of advertisements or learning the effectiveness of drugs during testing. My research focuses on this theme of sequential decision making and its applications to machine learning and algorithmic economics. Discrete optimization is at the center stage of algorithms and has applications to different areas of computer science. A burst of activity in applying it to real world problems has happened recently because of models which deal with nonlinearity. An example is the sensor placement problem where the total area covered by the sensors depends on their locations in a nonlinear manner. My research
Locally Adaptive Optimization: Adaptive Seeding for Monotone Submodular Functions
"... The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as they become accessible in order to maximize a global objec ..."
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The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as they become accessible in order to maximize a global objective function. More generally, adaptive seeding is a stochastic optimization framework where the choices in the first stage affect the realizations in the second stage, over which we aim to optimize. Our main result is a (1−1/e)2approximation for the adaptive seeding problem for any monotone submodular function. While adaptive policies are often approximated via nonadaptive policies, our algorithm is based on a novel method we call locallyadaptive policies. These policies combine a nonadaptive global structure, with local adaptive optimizations. This method enables the (1−1/e)2approximation for general monotone submodular functions and circumvents some of the impossibilities associated with nonadaptive policies. We also introduce a fundamental problem in submodular optimization that may be of independent interest: given a ground set of elements where every element appears with some small probability, find a set of expected size at most k that has the highest expected value over the realization of the elements. We show a surprising result: there are classes of monotone submodular functions (including coverage) that can be approximated almost optimally as the probability vanishes. For general monotone submodular functions we show via a reduction from PlantedClique that approximations for this problem are not likely to be obtainable. This optimization problem is an important tool for adaptive seeding via nonadaptive policies, and its hardness motivates the introduction of locallyadaptive policies we use in the main result.