It is well known that the problem of finding a maximum-weight base of matroid can be solved by a greedy algorithm. The aim of this paper is to extend this result for some more general problems. One of these problems i...
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It is well known that the problem of finding a maximum-weight base of matroid can be solved by a greedy algorithm. The aim of this paper is to extend this result for some more general problems. One of these problems is maximizing a linear objective function over a family 3 of integer nonnegative vectors. We establish a number of necessary and sufficient conditions for the greedy algorithm to find an optimal solution in the general and some special cases. For the Boolean case, Goecke et al. (in: Combinatorial Optimization, Lecture Notes in Mathematics, Vol. 1403, Springer, Berlin, 1986, p. 1986) proved that the algorithm works if and only if the so-called strong exchange property holds. We extend this result to a class of non-Boolean vector systems. (C) 2002 Elsevier B.V. All rights reserved.
greedy algorithm (GA) is an efficient sparse representation framework with numerous applications in machine learning and computer vision. However, conventional GA methods may fail when applied to grossly corrupted dat...
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greedy algorithm (GA) is an efficient sparse representation framework with numerous applications in machine learning and computer vision. However, conventional GA methods may fail when applied to grossly corrupted data because they iteratively estimate the sparse signal using least squares regression, which is sensitive to gross corruption and outliers. In this paper, we propose a modal regression based greedy algorithm referred as MROMP (modal regression based orthogonal matching pursuit) to robustly learn the sparse signal from corrupted measurements. Unlike previous GA methods, MROMP is based on sparse modal regression, which has decent robustness to heavy-tailed noise and outliers. To efficiently optimize MROMP, we devise two half-quadratic based algorithms with guaranteed convergence. Our another two contributions are leveraging MROMP to develop a robust subspace clustering method to cluster data lying in a union of subspaces, and a robust pattern classification method to recognize data into the class that they belong to, respectively. The experimental results on both simulated and real datasets demonstrate the efficacy and robustness of MROMP for sparse signal recovery, data clustering and classification, especially for grossly corrupted data. (C) 2019 Elsevier B.V. All rights reserved.
A neighbor system, introduced in this paper, is a collection of integral vectors in R-n with some special structure. Such collections (slightly) generalize jump systems, which, in turn, generalize integral bisubmodula...
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A neighbor system, introduced in this paper, is a collection of integral vectors in R-n with some special structure. Such collections (slightly) generalize jump systems, which, in turn, generalize integral bisubmodular polyhedra, integral polymatroids, delta-matroids, matroids, and other structures. We show that neighbor systems provide a systematic and simple way to characterize these structures. One of our main results is a simple greedy algorithm for optimizing over (finite) neighbor systems starting from any feasible vector. The algorithm is (essentially) identical to the usual greedy algorithm on matroids and integral polymatroids when the starting vector is zero. But in all other cases, from matroids through jump systems, it appears to be a new greedy algorithm. We end the paper by introducing another structure, which is more general than neighbor systems, and indicate that essentially the same greedy algorithm also works for this structure.
In this paper, we consider a greedy algorithm for thickness of graphs. The greedy algorithm we consider here takes a maximum planar subgraph away from the current graph in each iteration and repeats this process until...
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In this paper, we consider a greedy algorithm for thickness of graphs. The greedy algorithm we consider here takes a maximum planar subgraph away from the current graph in each iteration and repeats this process until the current graph has no edge. The greedy algorithm outputs the number of iterations which is an upper bound of thickness for an input graph G=(V, E). We show that the performance ratio of the greedy algorithm is Omega(log \V\). (C) 2002 Elsevier Science B.V. All rights reserved.
The density-based clustering algorithm presented is different from the classical Density-Based Spatial Clustering of Applications with Noise (DBSCAN) (Ester et al., 1996), and has the following advantages: first, Gree...
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The density-based clustering algorithm presented is different from the classical Density-Based Spatial Clustering of Applications with Noise (DBSCAN) (Ester et al., 1996), and has the following advantages: first, greedy algorithm substitutes for R*-tree (Bechmann et al., 1990) in DBSCAN to index the clustering space so that the clustering time cost is decreased to great extent and I/O memory load is reduced as well; second, the merging condition to approach to arbitrary-shaped clusters is designed carefully so that a single threshold can distinguish correctly all clusters in a large spatial dataset though some density-skewed clusters live in it. Finally, authors investigate a robotic navigation and test two artificial datasets by the proposed algorithm to verify its effectiveness and efficiency.
Compressed sensing (CS) has been one of the great successes of applied mathematics in the last decade. This paper proposes a new method, combining the advantage of the Compressive Sampling Matching Pursuit (CoSaMP) al...
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Compressed sensing (CS) has been one of the great successes of applied mathematics in the last decade. This paper proposes a new method, combining the advantage of the Compressive Sampling Matching Pursuit (CoSaMP) algorithm and the Quasi-Newton Iteration Projection (QNIP) algorithm, for the recovery of sparse signal from underdetermined linear systems. To get the new algorithm, Quasi-Newton Projection Pursuit (QNPP), the least-squares technique in CoSaMP is used to accelerate convergence speed and QNIP is modified slightly. The convergence rate of QNPP is studied, under a certain condition on the restricted isometry constant of the measurement matrix, which is smaller than that of QNIP. The fast version of QNPP is also proposed which uses the Richardson's iteration to reduce computation time. The numerical results show that the proposed algorithms have higher recovery rate and faster convergence speed than existing techniques. (c) 2017 Elsevier B.V. All rights reserved.
Mesh Deformation is an important element of any fluid-structure interaction simulation. In this article, a new methodology is presented for the deformation of volume meshes using incremental radial basis function (RBF...
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Mesh Deformation is an important element of any fluid-structure interaction simulation. In this article, a new methodology is presented for the deformation of volume meshes using incremental radial basis function (RBF) based interpolation. A greedy algorithm is used to select a small subset of the surface nodes iteratively. Two incremental approaches are introduced to solve the RBF system of equations: 1) block matrix inversion based approach and 2) modified LU decomposition approach. The use of incremental approach decreased the computational complexity of solving the system of equations within each greedy algorithm's iteration from O(n(3)) to O( n(2)). Results are presented from an accuracy study using specified deformations on a 2D surface. Mesh deformations for bending and twisting of a 3D rectangular supercritical wing have been demonstrated. Outcomes showed the incremental approaches reduce the CPU time up to 67% as compared to a traditional RBF matrix solver. Finally, the proposed mesh deformation approach was integrated within a fluid-structure interaction solver for investigating a flow induced cantilever beam vibration. (C) 2017 Elsevier Inc. All rights reserved.
We consider the assortment optimization problem under the classical two-level nested logit model. We establish a necessary and sufficient condition for the optimal assortment and develop a simple and fast greedy algor...
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We consider the assortment optimization problem under the classical two-level nested logit model. We establish a necessary and sufficient condition for the optimal assortment and develop a simple and fast greedy algorithm that iteratively removes at most one product from each nest to compute an optimal solution. (C) 2014 Elsevier B.V. All rights reserved.
Nowadays, using model checking techniques is one of the best solutions for software (and hardware) verification. The problem while using model checking techniques is state space explosion in which all the available me...
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Nowadays, using model checking techniques is one of the best solutions for software (and hardware) verification. The problem while using model checking techniques is state space explosion in which all the available memory is consumed by the model checker to generate all the reachable states. Among different approaches to cope with the state space explosion problem, using heuristic and meta-heuristic algorithms seems a proper solution. Although in all of these approaches it is not possible to solve the problem totally, however, it is possible to use them as refutation techniques. In the meta-heuristic techniques it is tried to generate only a portion of the state space with the highest probability to reach a faulty state. In this paper, we propose two new algorithms to deadlock detection in complex software systems specified through graph transformation systems. The first approach is a hybrid algorithm using PSO and BAT (BAPSO) and the second one is a greedy algorithm to find deadlocks. The experimental results show that the hybrid approach (BAPSO) is more accurate than PSO, BAT and other existing approaches like Genetic algorithm (GA). In addition, in most of the case studies, the proposed greedy algorithm can compete with the meta-heuristic algorithms in terms of speed and accuracy.
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