Greedy algorithm

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

Seismic data interpolation by greedy local Radon transform

Abstract: We propose a greedy inversion method for a spatially localized, high-resolution Radon transform. The kernel of the method is based on a conventional iterative algorithm, conjugate gradient (CG), but is utilized adaptively in amplitude-prioritized local model spaces. The adaptive inversion introduces a coherence-oriented mechanism to enhance focusing of significant model parameters, and hence increases the model resolution and convergence rate. We adopt the idea in a time-space domain local linear Radon transform for data interpolation. We find that the local Radon transform involves iteratively applying spatially localized forward and adjoint Radon operators to fit the input data. Optimal local Radon panels can be found via a subspace algorithm which promotes sparsity in the model, and the missing data can be predicted using the resulting local Radon panels. The subspacing strategy greatly reduces the cost of computing local Radon coefficients, thereby reducing the total cost for inversion. The method can handle irregular and regular geometries and significant spatial aliasing. We compare the performance of our method using three simple synthetic data sets with a popular interpolation method known as minimum weighted norm Fourier interpolation, and show the advantage of the new algorithm in interpolating spatially aliased data. We also test the algorithm on the 2D synthetic data and a field data set. Both tests show that the algorithm is a robust antialiasing tool, although it cannot completely recover missing strongly curved events.

Information theoretic sensor management

Abstract: Sensor management may be defined as those stochastic control problems in which control values are selected to influence sensing parameters in order to maximize the utility of the resulting measurements for an underlying detection or estimation problem. While problems of this type can be formulated as a dynamic program, the state space of the program is in general infinite, and traditional solution techniques are inapplicable. Despite this fact, many authors have applied simple heuristics such as greedy or myopic controllers with great success. This thesis studies sensor management problems in which information theoretic quantities such as entropy are utilized to measure detection or estimation performance. The work has two emphases: firstly, we seek performance bounds which guarantee per formance of the greedy heuristic and derivatives thereof in certain classes of problems. Secondly, we seek to extend these basic heuristic controllers to find algorithms that provide improved performance and are applicable in larger classes of problems for which the performance bounds do not apply. The primary problem of interest is multiple object tracking and identification; application areas include sensor network management and multifunction radar control. Utilizing the property of submodularity, as proposed for related problems by different authors, we show that the greedy heuristic applied to sequential selection problems with information theoretic objectives is guaranteed to achieve at least half of the optimal reward. Tighter guarantees are obtained for diffusive problems and for problems involving discounted rewards. Online computable guarantees also provide tighter bounds in specific problems. The basic result applies to open loop selections, where all decisions are made before any observation values are received; we also show that the closed loop greedy heuristic, which utilizes observations received in the interim in its subsequent decisions, possesses the same guarantee relative to the open loop optimal, and that no such guarantee exists relative to the optimal closed loop performance. The same mathematical property is utilized to obtain an algorithm that exploits the structure of selection problems involving multiple independent objects. The algorithm involves a sequence of integer programs which provide progressively tighter upper bounds to the true optimal reward. An auxiliary problem provides progressively tighter lower bounds, which can be used to terminate when a near-optimal solution has been found. The formulation involves an abstract resource consumption model, which allows observations that expend different amounts of available time. Finally, we present a heuristic approximation for an object tracking problem in a sensor network, which permits a direct trade-off between estimation performance and energy consumption. We approach the trade-off through a constrained optimization framework, seeking to either optimize estimation performance over a rolling horizon subject to a constraint on energy consumption, or to optimize energy consumption subject to a constraint on estimation performance. Lagrangian relaxation is used alongside a series of heuristic approximations to find a tractable solution that captures the essential structure in the problem.

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.

Technical Note—An Effective Heuristic for the M-Tour Traveling Salesman Problem with Some Side Conditions

Abstract: This note presents a heuristic for determining very good solutions for the symmetric M-tour traveling salesman problem with some side conditions. These side conditions' pertain to load, distance and time, or sequencing restrictions. The heuristic is an extension of the highly successful one of Lin and Kernighan for the single traveling salesman problem. Computational experience with widely tested vehicle dispatch problems indicates that the proposed heuristic consistently yields better solutions than existing heuristics that have appeared in the literature. Run times grow approximately as N2.3, where N is the number of cities. The heuristic is generally slower than the modified SWEEP heuristic except on problems having a large number of points per route.

Power-aware resource allocation for independent tasks in heterogeneous real-time systems

Abstract: In recent years, power management and power reduction has become a critical issue in portable systems that are designed for real-time use. In this paper, we study the problem of static allocation of a set of independent tasks onto a real-time system consisting of heterogeneous processing elements, each enabled with discrete Dynamic Voltage Scaling. The allocation problem is first formulated as an extended Generalized Assignment Problem. A linearization heuristic (LR-heuristic) is then extended for solving the problem. An analysis of the upper bound on the number of tasks that the heuristic may fail to allocate is also presented. Our experiments show that when the real-time constraints are tight, the LR-heuristic achieves 15% off the optimal energy consumption for small size problems, while the performance of a classic greedy heuristic is around 90% off the optimal. A relative performance improvement of up-to 40% over the classic greedy heuristic is also observed for large size problems.