It is well known that the greedy algorithm solves matroid base problems for all linear cost functions and is, in fact, correct if and only if the underlying combinatorial structure of the problem is a matroid. Moreove...
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It is well known that the greedy algorithm solves matroid base problems for all linear cost functions and is, in fact, correct if and only if the underlying combinatorial structure of the problem is a matroid. Moreover, the algorithm can be applied to problems with sum, bottleneck, algebraic sum or k-sum objective functions. In this paper, we address matroid base problems with a more general - "universal" - objective function which contains the previous ones as special cases. This universal objective function is of the sum type and associates multiplicative weights with the ordered cost coefficients of the elements of matroid bases such that, by choosing appropriate weights, many different - classical and new - objectives can be modeled. We show that the greedy algorithm is applicable to a larger class of objective functions than commonly known and, as such, it solves universal matroid base problems with non-negative or non-positive weight coefficients. Based on problems with mixed weights and a single (-, +)- sign change in the universal weight vector, we give a characterization of uniform matroids. In case of multiple sign changes, we use partition matroids. For non-uniform matroids, single sign change problems can be reduced to problems in minors obtained by deletion and contraction. Finally, we discuss how special instances of universal bipartite matching and shortest path problems can be tackled by applying greedy algorithms to associated transversal matroids. (C) 2014 Elsevier B.V. All rights reserved.
In this paper, we present a greedy algorithm based on a tensor product decomposition, whose aim is to compute the global minimum of a strongly convex energy functional. We prove the convergence of our method provided ...
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In this paper, we present a greedy algorithm based on a tensor product decomposition, whose aim is to compute the global minimum of a strongly convex energy functional. We prove the convergence of our method provided that the gradient of the energy is Lipschitz on bounded sets. The main interest of this method is that it can be used for high-dimensional nonlinear convex problems. We illustrate this method on a prototypical example for uncertainty propagation on the obstacle problem.
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.
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.
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.
To save energy and alleviate interference in a wireless sensor network, connected dominating set (CDS) has been proposed as the virtual backbone. Since nodes may fail due to accidental damage or energy depletion, it i...
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To save energy and alleviate interference in a wireless sensor network, connected dominating set (CDS) has been proposed as the virtual backbone. Since nodes may fail due to accidental damage or energy depletion, it is desirable to construct a fault tolerant CDS, which can be modeled as a -connected -fold dominating set -CDS for short): a subset of nodes is a -CDS of if every node in is adjacent with at least nodes in and the subgraph of induced by is -*** this paper, we present an approximation algorithm for the minimum -CDS problem with . Based on a -CDS, the algorithm greedily merges blocks until the connectivity is raised to two. The most difficult problem in the analysis is that the potential function used in the greedy algorithm is not submodular. By proving that an optimal solution has a specific decomposition, we managed to prove that the approximation ratio is , where is the approximation ratio for the minimum -CDS problem. This improves on previous approximation ratios for the minimum -CDS problem, both in general graphs and in unit disk graphs.
This paper proposes a new greedy algorithm combining the semi-supervised learning and the sparse representation with the data-dependent hypothesis spaces. The proposed greedy algorithm is able to use a small portion o...
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This paper proposes a new greedy algorithm combining the semi-supervised learning and the sparse representation with the data-dependent hypothesis spaces. The proposed greedy algorithm is able to use a small portion of the labeled and unlabeled data to represent the target function, and to efficiently reduce the computational burden of the semi-supervised learning. We establish the estimation of the generalization error based on the empirical covering numbers. A detailed analysis shows that the error has O(n(-1)) decay. Our theoretical result illustrates that the unlabeled data is useful to improve the learning performance under mild conditions. (C) 2013 Elsevier Ltd. All rights reserved.
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.
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