Greedy algorithm

About: Greedy algorithm is a research topic. Over the lifetime, 15347 publications have been published within this topic receiving 393945 citations.

Leader selection for optimal network coherence

Abstract: We consider the problem of leader-based distributed coordination in networks where agents are subject to stochastic disturbances, but where certain designated leaders are immune to those disturbances. Specifically, we address the effect of leader selection on the coherence of the network, defined in terms of an H 2 norm of the system. This quantity captures the level of agreement of the nodes in the face of the external disturbances. We show that network coherence depends on the eigenvalues of a principal submatrix of the Laplacian matrix, and we formulate an optimization problem to select the set of leaders that results in the highest coherence. As this optimization problem is combinatorial in nature, we also present several greedy algorithms for leader selection that rely on more easily computable bounds of the H 2 norm and the eigenvalues of the system. Finally, we illustrate the effectiveness of these algorithms using several network examples.

Reducing Controversy by Connecting Opposing Views

Abstract: Society is often polarized by controversial issues that split the population into groups with opposing views. When such issues emerge on social media, we often observe the creation of `echo chambers', i.e., situations where like-minded people reinforce each other's opinion, but do not get exposed to the views of the opposing side. In this paper we study algorithmic techniques for bridging these chambers, and thus reduce controversy. Specifically, we represent the discussion on a controversial issue with an endorsement graph, and cast our problem as an edge-recommendation problem on this graph. The goal of the recommendation is to reduce the controversy score of the graph, which is measured by a recently-developed metric based on random walks. At the same time, we take into account the acceptance probability of the recommended edge, which represents how likely the edge is to materialize in the endorsement graph. We propose a simple model based on a recently-developed user-level controversy score, that is competitive with state-of-the-art link-prediction algorithms. Our goal then becomes finding the edges that produce the largest reduction in the controversy score, in expectation. To solve this problem, we propose an efficient algorithm that considers only a fraction of all the possible combinations of edges. Experimental results show that our algorithm is more efficient than a simple greedy heuristic, while producing comparable score reduction. Finally, a comparison with other state-of-the-art edge-addition algorithms shows that this problem is fundamentally different from what has been studied in the literature.

Approximation Algorithms for Maximum Coverage and Max Cut with Given Sizes of Parts

Abstract: In this paper we demonstrate a general method of designing constant-factor approximation algorithms for some discrete optimization problems with cardinality constraints The core of the method is a simple deterministic ("pipage") procedure of rounding of linear relaxations By using the method we design a (1-(1-1/k)k)-approximation algorithm for the maximum coverage problem where k is the maximum size of the subsets that are covered, and a 1/2-approximation algorithm for the maximum cut problem with given sizes of parts in the vertex set bipartition The performance guarantee of the former improves on that of the well-known (1 - e-1)-greedy algorithm due to Cornuejols, Fisher and Nemhauser in each case of bounded k The latter is, to the best of our knowledge, the first constant-factor algorithm for that version of the maximum cut problem

Learning with dynamic group sparsity

Abstract: This paper investigates a new learning formulation called dynamic group sparsity. It is a natural extension of the standard sparsity concept in compressive sensing, and is motivated by the observation that in some practical sparse data the nonzero coefficients are often not random but tend to be clustered. Intuitively, better results can be achieved in these cases by reasonably utilizing both clustering and sparsity priors. Motivated by this idea, we have developed a new greedy sparse recovery algorithm, which prunes data residues in the iterative process according to both sparsity and group clustering priors rather than only sparsity as in previous methods. The proposed algorithm can recover stably sparse data with clustering trends using far fewer measurements and computations than current state-of-the-art algorithms with provable guarantees. Moreover, our algorithm can adaptively learn the dynamic group structure and the sparsity number if they are not available in the practical applications. We have applied the algorithm to sparse recovery and background subtraction in videos. Numerous experiments with improved performance over previous methods further validate our theoretical proofs and the effectiveness of the proposed algorithm.

Near-Optimal Bayesian Active Learning with Noisy Observations

Abstract: We tackle the fundamental problem of Bayesian active learning with noise, where we need to adaptively select from a number of expensive tests in order to identify an unknown hypothesis sampled from a known prior distribution. In the case of noise-free observations, a greedy algorithm called generalized binary search (GBS) is known to perform near-optimally. We show that if the observations are noisy, perhaps surprisingly, GBS can perform very poorly. We develop EC2, a novel, greedy active learning algorithm and prove that it is competitive with the optimal policy, thus obtaining the first competitiveness guarantees for Bayesian active learning with noisy observations. Our bounds rely on a recently discovered diminishing returns property called adaptive submodularity, generalizing the classical notion of submodular set functions to adaptive policies. Our results hold even if the tests have non-uniform cost and their noise is correlated. We also propose EFFECX-TIVE, a particularly fast approximation of EC2, and evaluate it on a Bayesian experimental design problem involving human subjects, intended to tease apart competing economic theories of how people make decisions under uncertainty.