Showing papers on "Greedy algorithm published in 2013"

FemtoCaching: Wireless Content Delivery Through Distributed Caching Helpers

Abstract: Video on-demand streaming from Internet-based servers is becoming one of the most important services offered by wireless networks today. In order to improve the area spectral efficiency of video transmission in cellular systems, small cells heterogeneous architectures (e.g., femtocells, WiFi off-loading) are being proposed, such that video traffic to nomadic users can be handled by short-range links to the nearest small cell access points (referred to as “helpers”). As the helper deployment density increases, the backhaul capacity becomes the system bottleneck. In order to alleviate such bottleneck we propose a system where helpers with low-rate backhaul but high storage capacity cache popular video files. Files not available from helpers are transmitted by the cellular base station. We analyze the optimum way of assigning files to the helpers, in order to minimize the expected downloading time for files. We distinguish between the uncoded case (where only complete files are stored) and the coded case, where segments of Fountain-encoded versions of the video files are stored at helpers. We show that the uncoded optimum file assignment is NP-hard, and develop a greedy strategy that is provably within a factor 2 of the optimum. Further, for a special case we provide an efficient algorithm achieving a provably better approximation ratio of 1-(1-1/d )d, where d is the maximum number of helpers a user can be connected to. We also show that the coded optimum cache assignment problem is convex that can be further reduced to a linear program. We present numerical results comparing the proposed schemes.

Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model

Abstract: The synthesis-based sparse representation model for signals has drawn considerable interest in the past decade. Such a model assumes that the signal of interest can be decomposed as a linear combination of a few atoms from a given dictionary. In this paper we concentrate on an alternative, analysis-based model, where an analysis operator-hereafter referred to as the analysis dictionary-multiplies the signal, leading to a sparse outcome. Our goal is to learn the analysis dictionary from a set of examples. The approach taken is parallel and similar to the one adopted by the K-SVD algorithm that serves the corresponding problem in the synthesis model. We present the development of the algorithm steps: This includes tailored pursuit algorithms-the Backward Greedy and the Optimized Backward Greedy algorithms, and a penalty function that defines the objective for the dictionary update stage. We demonstrate the effectiveness of the proposed dictionary learning in several experiments, treating synthetic data and real images, and showing a successful and meaningful recovery of the analysis dictionary.

Minimal Controllability Problems

Abstract: Given a linear system, we consider the problem of finding a small set of variables to affect with an input so that the resulting system is controllable. We show that this problem is NP-hard; indeed, we show that even approximating the minimum number of variables that need to be affected within a multiplicative factor of $c \log n$ is NP-hard for some positive $c$. On the positive side, we show it is possible to find sets of variables matching this inapproximability barrier in polynomial time. This can be done by a simple greedy heuristic which sequentially picks variables to maximize the rank increase of the controllability matrix. Experiments on Erdos-Renyi random graphs demonstrate this heuristic almost always succeeds at findings the minimum number of variables.

Greedy feature selection for subspace clustering

Abstract: Unions of subspaces provide a powerful generalization of single subspace models for collections of high-dimensional data; however, learning multiple subspaces from data is challenging due to the fact that segmentation--the identification of points that live in the same subspace--and subspace estimation must be performed simultaneously. Recently, sparse recovery methods were shown to provide a provable and robust strategy for exact feature selection (EFS)--recovering subsets of points from the ensemble that live in the same subspace. In parallel with recent studies of EFS with l1-minimization, in this paper, we develop sufficient conditions for EFS with a greedy method for sparse signal recovery known as orthogonal matching pursuit (OMP). Following our analysis, we provide an empirical study of feature selection strategies for signals living on unions of subspaces and characterize the gap between sparse recovery methods and nearest neighbor (NN)-based approaches. In particular, we demonstrate that sparse recovery methods provide significant advantages over NN methods and that the gap between the two approaches is particularly pronounced when the sampling of subspaces in the data set is sparse. Our results suggest that OMP may be employed to reliably recover exact feature sets in a number of regimes where NN approaches fail to reveal the subspace membership of points in the ensemble.

NETAL: a new graph-based method for global alignment of protein–protein interaction networks

Abstract: Motivation: The interactions among proteins and the resulting networks of such interactions have a central role in cell biology. Aligning these networks gives us important information, such as conserved complexes and evolutionary relationships. Although there have been several publications on the global alignment of protein networks; however, none of proposed methods are able to produce a highly conserved and meaningful alignment. Moreover, time complexity of current algorithms makes them impossible to use for multiple alignment of several large networks together. Results: We present a novel algorithm for the global alignment of protein–protein interaction networks. It uses a greedy method, based on the alignment scoring matrix, which is derived from both biological and topological information of input networks to find the best global network alignment. NETAL outperforms other global alignment methods in terms of several measurements, such as Edge Correctness, Largest Common Connected Subgraphs and the number of common Gene Ontology terms between aligned proteins. As the running time of NETAL is much less than other available methods, NETAL can be easily expanded to multiple alignment algorithm. Furthermore, NETAL overpowers all other existing algorithms in term of performance so that the short running time of NETAL allowed us to implement it as the first server for global alignment of protein–protein interaction networks. Availability: Binaries supported on linux are freely available for download at http://www.bioinf.cs.ipm.ir/software/netal. Contact: sh.arab@modares.ac.ir Supplementary information: Supplementary data are available at Bioinformatics online.

Identifying influential nodes in complex networks with community structure

Abstract: It is a fundamental issue to find a small subset of influential individuals in a complex network such that they can spread information to the largest number of nodes in the network. Though some heuristic methods, including degree centrality, betweenness centrality, closeness centrality, the k-shell decomposition method and a greedy algorithm, can help identify influential nodes, they have limitations for networks with community structure. This paper reveals a new measure for assessing the influence effect based on influence scope maximization, which can complement the traditional measure of the expected number of influenced nodes. A novel method for identifying influential nodes in complex networks with community structure is proposed. This method uses the information transfer probability between any pair of nodes and the k-medoid clustering algorithm. The experimental results show that the influential nodes identified by the k-medoid method can influence a larger scope in networks with obvious community structure than the greedy algorithm without reducing the expected number of influenced nodes.

SIGMa: simple greedy matching for aligning large knowledge bases

Abstract: The Internet has enabled the creation of a growing number of large-scale knowledge bases in a variety of domains containing complementary information. Tools for automatically aligning these knowledge bases would make it possible to unify many sources of structured knowledge and answer complex queries. However, the efficient alignment of large-scale knowledge bases still poses a considerable challenge. Here, we present Simple Greedy Matching (SiGMa), a simple algorithm for aligning knowledge bases with millions of entities and facts. SiGMa is an iterative propagation algorithm that leverages both the structural information from the relationship graph and flexible similarity measures between entity properties in a greedy local search, which makes it scalable. Despite its greedy nature, our experiments indicate that SiGMa can efficiently match some of the world's largest knowledge bases with high accuracy. We provide additional experiments on benchmark datasets which demonstrate that SiGMa can outperform state-of-the-art approaches both in accuracy and efficiency.

Submodular Salient Region Detection

Abstract: The problem of salient region detection is formulated as the well-studied facility location problem from operations research. High-level priors are combined with low-level features to detect salient regions. Salient region detection is achieved by maximizing a sub modular objective function, which maximizes the total similarities (i.e., total profits) between the hypothesized salient region centers (i.e., facility locations) and their region elements (i.e., clients), and penalizes the number of potential salient regions (i.e., the number of open facilities). The similarities are efficiently computed by finding a closed-form harmonic solution on the constructed graph for an input image. The saliency of a selected region is modeled in terms of appearance and spatial location. By exploiting the sub modularity properties of the objective function, a highly efficient greedy-based optimization algorithm can be employed. This algorithm is guaranteed to be at least a (e - 1)/e 0.632-approximation to the optimum. Experimental results demonstrate that our approach outperforms several recently proposed saliency detection approaches.

Computing sparse representations of multidimensional signals using kronecker bases

Abstract: Recently there has been great interest in sparse representations of signals under the assumption that signals data sets can be well approximated by a linear combination of few elements of a known basis dictionary. Many algorithms have been developed to find such representations for one-dimensional signals vectors, which requires finding the sparsest solution of an underdetermined linear system of algebraic equations. In this letter, we generalize the theory of sparse representations of vectors to multiway arrays tensors-signals with a multidimensional structure-by using the Tucker model. Thus, the problem is reduced to solving a large-scale underdetermined linear system of equations possessing a Kronecker structure, for which we have developed a greedy algorithm, Kronecker-OMP, as a generalization of the classical orthogonal matching pursuit OMP algorithm for vectors. We also introduce the concept of multiway block-sparse representation of N-way arrays and develop a new greedy algorithm that exploits not only the Kronecker structure but also block sparsity. This allows us to derive a very fast and memory-efficient algorithm called N-BOMP N-way block OMP. We theoretically demonstrate that under the block-sparsity assumption, our N-BOMP algorithm not only has a considerably lower complexity but is also more precise than the classic OMP algorithm. Moreover, our algorithms can be used for very large-scale problems, which are intractable using standard approaches. We provide several simulations illustrating our results and comparing our algorithms to classical algorithms such as OMP and BP basis pursuit algorithms. We also apply the N-BOMP algorithm as a fast solution for the compressed sensing CS problem with large-scale data sets, in particular, for 2D compressive imaging CI and 3D hyperspectral CI, and we show examples with real-world multidimensional signals.

Least Cost Rumor Blocking in Social Networks

Abstract: In many real-world scenarios, social network serves as a platform for information diffusion, alongside with positive information (truth) dissemination, negative information (rumor) also spread among the public. To make the social network as a reliable medium, it is necessary to have strategies to control rumor diffusion. In this article, we address the Least Cost Rumor Blocking (LCRB) problem where rumors originate from a community Cr in the network and a notion of protectors are used to limit the bad influence of rumors. The problem can be summarized as identifying a minimal subset of individuals as initial protectors to minimize the number of people infected in neighbor communities of Cr at the end of both diffusion processes. Observing the community structure property, we pay attention to a kind of vertex set, called bridge end set, in which each node has at least one direct in-neighbor in Cr and is reachable from rumors. Under the OOAO model, we study LCRB-P problem, in which α (0 <; α <; 1) fraction of bridge ends are required to be protected. We prove that the objective function of this problem is submodular and a greedy algorithm is adopted to derive a (1-1/e)-approximation. Furthermore, we study LCRB-D problem over the DOAA model, in which all the bridge ends are required to be protected, we prove that there is no polynomial time o(ln n)-approximation for the LCRB-D problem unless P = NP, and propose a Set Cover Based Greedy (SCBG) algorithm which achieves a O(ln n)-approximation ratio. Finally, to evaluate the efficiency and effectiveness of our algorithm, we conduct extensive comparison simulations in three real-world datasets, and the results show that our algorithm outperforms other heuristics.

Minimising makespan in distributed permutation flowshops using a modified iterated greedy algorithm

Abstract: The distributed permutation flowshop scheduling problem (DPFSP) is a newly proposed topic in the shop scheduling field, which has important application in globalised and multi-plant environments. This study presents a modified iterated greedy (MIG) algorithm for this problem to minimise the maximum completion time among all the factories. Compared with previous approaches, the proposed algorithm is simpler yet more effective, more efficient, and more robust in solving the DPFSP. To validate the performance of the proposed MIG algorithm, computational experiments and comparisons are conducted on an extended benchmark problem set of Taillard. Despite its simplicity, the computational results show that the proposed MIG algorithm outperforms all existing algorithms, and the best-known solutions for almost half of instances are updated. This study can be offered as a contribution to the growing body of work on both theoretically and practically useful approaches to the DPFSP.

On minimizing budget and time in influence propagation over social networks

Abstract: In recent years, study of influence propagation in social networks has gained tremendous attention. In this context, we can identify three orthogonal dimensions—the number of seed nodes activated at the beginning (known as budget), the expected number of activated nodes at the end of the propagation (known as expected spread or coverage), and the time taken for the propagation. We can constrain one or two of these and try to optimize the third. In their seminal paper, Kempe et al. constrained the budget, left time unconstrained, and maximized the coverage: this problem is known as Influence Maximization (or MAXINF for short). In this paper, we study alternative optimization problems which are naturally motivated by resource and time constraints on viral marketing campaigns. In the first problem, termed minimum target set selection (or MINTSS for short), a coverage threshold η is given and the task is to find the minimum size seed set such that by activating it, at least η nodes are eventually activated in the expected sense. This naturally captures the problem of deploying a viral campaign on a budget. In the second problem, termed MINTIME, the goal is to minimize the time in which a predefined coverage is achieved. More precisely, in MINTIME, a coverage threshold η and a budget threshold k are given, and the task is to find a seed set of size at most k such that by activating it, at least η nodes are activated in the expected sense, in the minimum possible time. This problem addresses the issue of timing when deploying viral campaigns. Both these problems are NP-hard, which motivates our interest in their approximation. For MINTSS, we develop a simple greedy algorithm and show that it provides a bicriteria approximation. We also establish a generic hardness result suggesting that improving this bicriteria approximation is likely to be hard. For MINTIME, we show that even bicriteria and tricriteria approximations are hard under several conditions. We show, however, that if we allow the budget for number of seeds k to be boosted by a logarithmic factor and allow the coverage to fall short, then the problem can be solved exactly in PTIME, i.e., we can achieve the required coverage within the time achieved by the optimal solution to MINTIME with budget k and coverage threshold η. Finally, we establish the value of the approximation algorithms, by conducting an experimental evaluation, comparing their quality against that achieved by various heuristics.

Convergence Rates of the POD–Greedy Method

Abstract: Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approxi- mating solution sets of parametrized partial differential equations. Recently, ap rioriconvergence rate statements for this algorithm have been given (Buffa et al. 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD-Greedy algorithm (Haasdonk and Ohlberger 2008). In this algorithm, each greedy step is invoking a temporal compression step by performing a proper orthogonal decomposition (POD). Using a suitable coefficient representation of the POD-Greedy algorithm, we show that the existing conver- gence rate results of the Greedy algorithm can be extended. In particular, exponential or algebraic convergence rates of the Kolmogorov n-widths are maintained by the POD-Greedy algorithm.

Chemical reaction optimization with greedy strategy for the 0-1 knapsack problem

Abstract: The 0-1 knapsack problem (KP01) is a well-known combinatorial optimization problem. It is an NP-hard problem which plays important roles in computing theory and in many real life applications. Chemical reaction optimization (CRO) is a new optimization framework, inspired by the nature of chemical reactions. CRO has demonstrated excellent performance in solving many engineering problems such as the quadratic assignment problem, neural network training, multimodal continuous problems, etc. This paper proposes a new chemical reaction optimization with greedy strategy algorithm (CROG) to solve KP01. The paper also explains the operator design and parameter turning methods for CROG. A new repair function integrating a greedy strategy and random selection is used to repair the infeasible solutions. The experimental results have proven the superior performance of CROG compared to genetic algorithm (GA), ant colony optimization (ACO) and quantum-inspired evolutionary algorithm (QEA).

Greedy sparsity-constrained optimization

Abstract: Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and Compressed Sensing. A vast body of work has studied the sparsity-constrained optimization from theoretical, algorithmic, and application aspects in the context of sparse estimation in linear models where the fidelity of the estimate is measured by the squared error. In contrast, relatively less effort has been made in the study of sparsity-constrained optimization in cases where nonlinear models are involved or the cost function is not quadratic. In this paper we propose a greedy algorithm, Gradient Support Pursuit (GraSP), to approximate sparse minima of cost functions of arbitrary form. Should a cost function have a Stable Restricted Hessian (SRH) or a Stable Restricted Linearization (SRL), both of which are introduced in this paper, our algorithm is guaranteed to produce a sparse vector within a bounded distance from the true sparse optimum. Our approach generalizes known results for quadratic cost functions that arise in sparse linear regression and Compressed Sensing. We also evaluate the performance of GraSP through numerical simulations on synthetic and real data, where the algorithm is employed for sparse logistic regression with and without l2-regularization.

StaticGreedy: solving the scalability-accuracy dilemma in influence maximization

Abstract: Influence maximization, defined as a problem of finding a set of seed nodes to trigger a maximized spread of influence, is crucial to viral marketing on social networks. For practical viral marketing on large scale social networks, it is required that influence maximization algorithms should have both guaranteed accuracy and high scalability. However, existing algorithms suffer a scalability-accuracy dilemma: conventional greedy algorithms guarantee the accuracy with expensive computation, while the scalable heuristic algorithms suffer from unstable accuracyIn this paper, we focus on solving this scalability-accuracy dilemma. We point out that the essential reason of the dilemma is the surprising fact that the submodularity, a key requirement of the objective function for a greedy algorithm to approximate the optimum, is not guaranteed in all conventional greedy algorithms in the literature of influence maximization. Therefore a greedy algorithm has to afford a huge number of Monte Carlo simulations to reduce the pain caused by unguaranteed submodularity. Motivated by this critical finding, we propose a static greedy algorithm, named StaticGreedy, to strictly guarantee the submodularity of influence spread function during the seed selection process. The proposed algorithm makes the computational expense dramatically reduced by two orders of magnitude without loss of accuracy. Moreover, we propose a dynamical update strategy which can speed up the StaticGreedy algorithm by 2-7 times on large scale social networks.

Energy-saving virtual machine placement in cloud data centers

Abstract: In cloud data centers, different mapping relationships between virtual machines (VMs) and physical machines (PMs) cause different resource utilization, therefore, how to place VMs on PMs to improve resource utilization and reduce energy consumption is one of the major concerns for cloud providers. The existing VM placement schemes are to optimize physical server resources utilization or network resources utilization, but few of them focuses on optimizing multiple resources utilization simultaneously. To address the issue, this paper proposes a VM placement scheme meeting multiple resource constraints, such as the physical server size (CPU, memory, storage, bandwidth, etc.) and network link capacity to improve resource utilization and reduce both the number of active physical servers and network elements so as to finally reduce energy consumption. Since VM placement problem is abstracted as a combination of bin packing problem and quadratic assignment problem, which is also known as a classic combinatorial optimization and NP-hard problem, we design a novel greedy algorithm by combining minimum cut with the best-fit, and the simulations show that our solution achieves better results.

Balancing bicycle sharing systems: a variable neighborhood search approach

Abstract: We consider the necessary redistribution of bicycles in public bicycle sharing systems in order to avoid rental stations to run empty or entirely full. For this purpose we propose a general Variable Neighborhood Search (VNS) with an embedded Variable Neighborhood Descent (VND) that exploits a series of neighborhood structures. While this metaheuristic generates candidate routes for vehicles to visit unbalanced rental stations, the numbers of bikes to be loaded or unloaded at each stop are efficiently derived by one of three alternative methods based on a greedy heuristic, a maximum flow calculation, and linear programming, respectively. Tests are performed on instances derived from real-world data and indicate that the VNS based on a greedy heuristic represents the best compromise for practice. In general the VNS yields good solutions and scales much better to larger instances than two mixed integer programming approaches.

Greedy Algorithms for Reduced Bases in Banach Spaces

Abstract: Given a Banach space X and one of its compact sets $\mathcal{F}$ , we consider the problem of finding a good n-dimensional space X n ⊂X which can be used to approximate the elements of $\mathcal{F}$ . The best possible error we can achieve for such an approximation is given by the Kolmogorov width $d_{n}(\mathcal{F})_{X}$ . However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Model. Math. Anal. Numer. 46:595–603, 2012) in the case $X=\mathcal{H}$ is a Hilbert space. The results of Buffa et al. (Model. Math. Anal. Numer. 46:595–603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457–1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces.

Portfolio greedy search and simulation for large-scale combat in starcraft

Abstract: Real-time strategy video games have proven to be a very challenging area for applications of artificial intelligence research. With their vast state and action spaces and real-time constraints, existing AI solutions have been shown to be too slow, or only able to be applied to small problem sets, while human players still dominate RTS AI systems. This paper makes three contributions to advancing the state of AI for popular commercial RTS game combat, which can consist of battles of dozens of units. First, we present an efficient system for modelling abstract RTS combat called SparCraft, which can perform millions of unit actions per second and visualize them. We then present a modification of the UCT algorithm capable of performing search in games with simultaneous and durative actions. Finally, a novel greedy search algorithm called Portfolio Greedy Search is presented which uses hill climbing and accurate playout-based evaluations to efficiently search even the largest combat scenarios. We demonstrate that Portfolio Greedy Search outperforms state of the art Alpha-Beta and UCT search methods for large StarCraft combat scenarios of up to 50 vs. 50 units under real-time search constraints of 40 ms per search episode.

QoS-Aware Data Replication for Data-Intensive Applications in Cloud Computing Systems

Abstract: Cloud computing provides scalable computing and storage resources. More and more data-intensive applications are developed in this computing environment. Different applications have different quality-of-service (QoS) requirements. To continuously support the QoS requirement of an application after data corruption, we propose two QoS-aware data replication (QADR) algorithms in cloud computing systems. The first algorithm adopts the intuitive idea of high-QoS first-replication (HQFR) to perform data replication. However, this greedy algorithm cannot minimize the data replication cost and the number of QoS-violated data replicas. To achieve these two minimum objectives, the second algorithm transforms the QADR problem into the well-known minimum-cost maximum-flow (MCMF) problem. By applying the existing MCMF algorithm to solve the QADR problem, the second algorithm can produce the optimal solution to the QADR problem in polynomial time, but it takes more computational time than the first algorithm. Moreover, it is known that a cloud computing system usually has a large number of nodes. We also propose node combination techniques to reduce the possibly large data replication time. Finally, simulation experiments are performed to demonstrate the effectiveness of the proposed algorithms in the data replication and recovery.

An Information-Theoretic Approach to PMU Placement in Electric Power Systems

Abstract: This paper presents an information-theoretic approach to address the phasor measurement unit (PMU) placement problem in electric power systems. Different from the conventional `topological observability' based approaches, this paper advocates a much more refined, information-theoretic criterion, namely the mutual information (MI) between PMU measurements and power system states. The proposed MI criterion not only includes observability as a special case, but also rigorously models the uncertainty reduction on power system states from PMU measurements. Thus, it can generate highly informative PMU configurations. The MI criterion can also facilitate robust PMU placement by explicitly modeling probabilistic PMU outages. We propose a greedy PMU placement algorithm, and show that it achieves an approximation ratio of (1-1/e) for any PMU placement budget. We further show that the performance is the best that one can achieve, in the sense that it is NP-hard to achieve any approximation ratio beyond (1-1/e) . Such performance guarantee makes the greedy algorithm very attractive in the practical scenario of multi-stage installations for utilities with limited budgets. Finally, simulation results demonstrate near-optimal performance of the proposed PMU placement algorithm.

The Exact Support Recovery of Sparse Signals With Noise via Orthogonal Matching Pursuit

Abstract: Orthogonal matching pursuit (OMP) algorithm is a classical greedy algorithm in Compressed Sensing. In this letter, we study the performance of OMP in recovering the support of a sparse signal from a few noisy linear measurements. We consider two types of bounded noise and our analysis is in the framework of restricted isometry property (RIP). It is shown that under some conditions on RIP and the minimum magnitude of the nonzero elements of the sparse signal, OMP with proper stopping rules can recover the support of the signal exactly from the noisy observation. We also discuss the case of Gaussian noise. Our conditions on RIP improve some existing results.

Advances in Bayesian network learning using integer programming

Abstract: We consider the problem of learning Bayesian networks (BNs) from complete discrete data This problem of discrete optimisation is formulated as an integer program (IP) We describe the various steps we have taken to allow efficient solving of this IP These are (i) efficient search for cutting planes, (ii) a fast greedy algorithm to find high-scoring (perhaps not optimal) BNs and (iii) tightening the linear relaxation of the IP After relating this BN learning problem to set covering and the multidimensional 0-1 knapsack problem, we present our empirical results These show improvements, sometimes dramatic, over earlier results

Ant colony optimization algorithm with pheromone correction strategy for the minimum connected dominating set problem

Abstract: In this paper an ant colony optimization (ACO) algorithm for the minimum connected dominating set problem (MCDSP) is presented. The MCDSP become increasingly important in recent years due to its applicability to the mobile ad hoc networks (MANETs) and sensor grids. We have implemented a one-step ACO algorithm based on a known simple greedy algorithm that has a significant drawback of being easily trapped in local optima. We have shown that by adding a pheromone correction strategy and dedicating special attention to the initial condition of the ACO algorithm this negative effect can be avoided. Using this approach it is possible to achieve good results without using the complex two-step ACO algorithm previously developed. We have tested our method on standard benchmark data and shown that it is competitive to the existing algorithms.

Double Greedy Algorithms: Reduced Basis Methods for Transport Dominated Problems

Abstract: The central objective of this paper is to develop reduced basis methods for parameter dependent transport dominated problems that are rigorously proven to exhibit rate-optimal performance when compared with the Kolmogorov $n$-widths of the solution sets. The central ingredient is the construction of computationally feasible "tight" surrogates which in turn are based on deriving a suitable well-conditioned variational formulation for the parameter dependent problem. The theoretical results are illustrated by numerical experiments for convection-diffusion and pure transport equations. In particular, the latter example sheds some light on the smoothness of the dependence of the solutions on the parameters.

Robust principal component analysis via capped norms

Abstract: In many applications such as image and video processing, the data matrix often possesses simultaneously a low-rank structure capturing the global information and a sparse component capturing the local information. How to accurately extract the low-rank and sparse components is a major challenge. Robust Principal Component Analysis (RPCA) is a general framework to extract such structures. It is well studied that under certain assumptions, convex optimization using the trace norm and l1-norm can be an effective computation surrogate of the difficult RPCA problem. However, such convex formulation is based on a strong assumption which may not hold in real-world applications, and the approximation error in these convex relaxations often cannot be neglected. In this paper, we present a novel non-convex formulation for the RPCA problem using the capped trace norm and the capped l1-norm. In addition, we present two algorithms to solve the non-convex optimization: one is based on the Difference of Convex functions (DC) framework and the other attempts to solve the sub-problems via a greedy approach. Our empirical evaluations on synthetic and real-world data show that both of the proposed algorithms achieve higher accuracy than existing convex formulations. Furthermore, between the two proposed algorithms, the greedy algorithm is more efficient than the DC programming, while they achieve comparable accuracy.

Fast greedy algorithms in mapreduce and streaming

Abstract: Greedy algorithms are practitioners' best friends - they are intuitive, simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advantage of the extra processing power.Our main result is a powerful sampling technique that aids in parallelization of sequential algorithms. We then show how to use this primitive to adapt a broad class of greedy algorithms to the MapReduce paradigm; this class includes maximum cover and submodular maximization subject to p-system constraints. Our method yields efficient algorithms that run in a logarithmic number of rounds, while obtaining solutions that are arbitrarily close to those produced by the standard sequential greedy algorithm. We begin with algorithms for modular maximization subject to a matroid constraint, and then extend this approach to obtain approximation algorithms for submodular maximization subject to knapsack or p-system constraints. Finally, we empirically validate our algorithms, and show that they achieve the same quality of the solution as standard greedy algorithms but run in a substantially fewer number of rounds.