Minimum Inverse Research Articles

A Weighted Inverse Minimum s − t Cut Problem with Value Constraint Under the Bottleneck-Type Hamming Distance

Given a network [Formula: see text] and an [Formula: see text] cut [Formula: see text] with the capacity [Formula: see text] and the constant value [Formula: see text], an inverse minimum [Formula: see text] cut problem with value constraint is to modify the vector capacity [Formula: see text] as little as possible to make the [Formula: see text] cut [Formula: see text] become a minimum [Formula: see text] cut with the capacity [Formula: see text]. The distinctive feature of this problem with the inverse minimum cut problems is the addition of a constraint in which the capacity of the given cut has to equal to the preassumed value [Formula: see text]. In this paper, we investigate the inverse minimum [Formula: see text] cut problem with value constraint under the bottleneck weighted Hamming distance. We propose two strongly polynomial time algorithms based on a binary search to solve the problem. At each iteration of the first one, we solve a feasible flow problem. The second algorithm considers the problem in two cases [Formula: see text] and [Formula: see text]. In this algorithm, we first modify the capacity vector such that the given cut becomes a minimum [Formula: see text] cut in the network and then, by preserving optimality this [Formula: see text] cut, adjust it to satisfy value constraint.

Constrained inverse minimum flow problems under the weighted Hamming distance

In an inverse combinatorial optimization problem, a feasible solution is given and is not optimal under the current parameters. The aim is to make the feasible solution optimal by modifying the current parameters as little as possible. The modification cost can be measured by different norms, such as weighted l1 norm, weighted l2 norm, weighted l∞ norm, weighted Hamming distance and so on.In this paper, we focus on the constrained inverse minimum flow problems under the weighted Hamming distance. Three different models are considered: the general problem under the weighted bottleneck-type Hamming distance and two cases under the mixed of sum-type and bottleneck type. Strongly polynomial algorithms are presented for the models we studied.

Partial inverse min–max spanning tree problem

This paper addresses a partial inverse combinatorial optimization problem, called the partial inverse min–max spanning tree problem. For a given weighted graph G and a forest F of the graph, the problem is to modify weights at minimum cost so that a bottleneck (min–max) spanning tree of G contains the forest. In this paper, the modifications are measured by the weighted Manhattan distance. The main contribution is to present two algorithms to solve the problem in polynomial time. This result is considerable because the partial inverse minimum spanning tree problem, which is closely related to this problem, is proved to be NP-hard in the literature. Since both the algorithms have the same worse-case complexity, some computational experiments are reported to compare their running time.

Inverse Minimum Cut Problem with Lower and Upper Bounds

The inverse minimum cut problem is one of the classical inverse optimization researches. In this paper, the inverse minimum cut with a lower and upper bounds problem is considered. The problem is to change both, the lower and upper bounds on arcs so that a given feasible cut becomes a minimum cut in the modified network and the distance between the initial vector of bounds and the modified one is minimized. A strongly polynomial algorithm to solve the problem under l1 norm is developed.

Inverse minimum flow problem under the weighted sum-type Hamming distance

The idea of the inverse optimization problem is to adjust the value of the parameters such that the observed feasible solution becomes optimal. The modification cost can be measured by different norms, such as l1,l2,l∞ norms and the Hamming distance, and the goal is to adjust the parameters as little as possible.In this paper, we consider the inverse minimum flow problem under the weighted sum-type Hamming distance, where the lower and upper bounds for the arcs should be changed as little as possible under the weighted sum-type Hamming distance such that a given feasible flow becomes a minimum flow. Two models are considered: the unbounded case and the general bounded case. We present their respective combinatorial algorithms that both run in O(nm) time in terms of the minimum cut method. Computational examples are presented to illustrate our algorithms.

Immediate Effects of Low-Dye Taping on the Ankle Motion and Ground Reaction Forces in the Pronated Rear-Foot During Gait

Background: Increased foot pronation causes biomedchanical changes at the lower limbs, which may result in musculoskeletal injuries at the proximal joints. Pronation rear-foot leads to plantar fasciitis, Achilles tendonitis, and posterior tibial tendonitis pathologically. According to the recent meta-analysis, They showed that therapeutic adhesive taping is more effective than foot orthoses and motion control footwear, low-Dye (LD) taping has become the most popular method used by physiotherapists. Objects: The purpose of this study was to determine the immediate effects of LD taping results in different ankle motion and ground reaction force (GRF) as before and after applied LD taping on pronated rear-foot during gait. Methods: Twenty-four participants were recruited for this study. The gait data were recorded using an 8-camera motion capture system and two force platforms. At first, the experiments were carried out that participants walked barefoot without LD taping. And then they walked both feet was applied LD taping. Results: The ankle inversion minimum was significantly greater after LD taping than before LD taping (p=.04); however, in the GRF, there were no significant differences in the inversion maximum or total motion of the stance phase (p=.33, p=.07), or in the vertical (p=.33), posterior (p=.22), and lateral (p=.14) peak forces. Conclusion: The application of taping to pronation rear-foot assists in increased ankle inversion.

On inverse linear programming problems under the bottleneck-type weighted Hamming distance

Given a linear programming problem with the objective function coefficients vector c and a feasible solution x0 to this problem, a corresponding inverse linear programming problem is to modify the vector c as little as possible to make x0 form an optimal solution to the linear programming problem. The modifications can be measured by different distances. In this article, we consider the inverse linear programming problem under the bottleneck-type weighted Hamming distance. We propose an algorithm based on the binary search technique to solve the problem. At each iteration, the algorithm has to solve a linear programming problem. We also consider the inverse minimum cost flow problem as a special case of the inverse linear programming problems and specialize the proposed method for solving this problem in strongly polynomial time. The specialized algorithm solves a shortest path problem at each iteration. It is shown that its complexity is better than the previous one.

Double zero minimum variance distortionless response beamformer

Adaptive beamformers (ABFs) place deep beampattern notches near interferers to suppress the interferers' power in the ABF output. The common sample matrix inversion (SMI) Minimum Variance Distortionless Response (MVDR) ABF computes the beamformer weights by substituting the sample covariance matrix (SCM) for the unknown ensemble covariance matrix in the MVDR expression. Errors in the SCM estimate of interferer direction due to limited sample support or interferer motion degrade the ABFs ability to suppress the interferer. This presentation exploits array polynomial properties to design a robust ABF. The array polynomial for a uniform linear array beamformer is the z-transform of the array weights. The array polynomial zeros on the unit circle correspond to the beampattern nulls. The proposed double zero (DZ) MVDR ABF solves for the MVDR weights using the SCM for a half-aperture subarray, then convolves the half-aperture weights with themselves to obtain the full aperture ABF weights. The resulting array polynomial for the DZ MVDR ABF has second-order zeros, producing broader and deeper notches in the interferer direction. The DZ MVDR ABF outperforms the SMI MVDR and covariance matrix tapered ABFs in simulations with stationary and moving interferers. [Work supported by ONR 321US.]

Capacity inverse minimum cost flow problems under the weighted Hamming distance

Given a network N(V, A, u, c) and a feasible flow \(x^0\), the inverse minimum cost flow problem is to modify the capacity vector or the cost vector as little as possible to make \(x^0\) form a minimum cost flow of the network. The modification can be measured by different norms. In this paper, we consider the capacity inverse minimum cost flow problems under the weighted Hamming distance, where we use the weighted Hamming distance to measure the modification of the arc capacities. Both the sum-type and the bottleneck-type cases are considered. For the former, it is shown to be APX-hard due to the weighted feedback arc set problem. For the latter, we present a strongly polynomial algorithm which can be done in \(O(n\cdot m^2)\) time.

States of maximum polarization for a quantum light field and states of a maximum sensitivity in quantum interferometry

The SU(2) group is used in two different fields of quantum optics, the quantum polarization and quantum interferometry. Quantum degrees of polarization may be based on distances of a polarization state from the set of unpolarized states. The maximum polarization is achieved in the case where the state is pure and then the distribution of the photon-number sums is optimized. In quantum interferometry, the SU(2) intelligent states have also the property that the Fisher measure of information is equal to the inverse minimum detectable phase shift on the usual simplifying condition. Previously, the optimization of the Fisher information under a constraint was studied. Now, in the framework of constraint optimization, states similar to the SU(2) intelligent states are treated.

レーリーの原理の逆問題型定式化に基づくせん断型構造物の剛性決定法

The shape, boundary conditions of the loads and displacements, and distributions of mass and stiffness of a continuum are given in classical variational principles, whereas an inverse variational principle deals with a type of problems where boundary shape is unknown. Another type of inverse formulation of variational principle proposed in this paper is applicable to sizing optimization or a stiffness identification problem. This paper discusses an inverse formulation of Rayleigh's principle that is useful to identify unknown stiffness for a given eigenvalue and eigenmode. An analytical example is employed to illustrate that the inverse minimum principle of potential energy proposed in this paper is useful in identifying discretized stiffness distribution of a shear structure having designated eigenvalue and eigenmode.

Note on the Inverse Metric Traveling Salesman Problem Against the Minimum Spanning Tree Algorithm

ABSTRACT In this paper, we consider an interesting variant of the inverse minimum traveling salesman problem. Given an in-stance ( G , w ) of the minimum traveling salesman problem defined on a metric space, we fix a specified Hamiltonian cycle HC 0 . The task is then to adjust the edge cost vector w to w ' so that the new cost vector w ' satisfies the triangle inequality condition and HC 0 can be returned by the minimum spanning tree algorithm in the TSP-instance defined with w '. The objective is to minimize the total deviation between the original and the new cost vectors with respect to the L 1 -norm. We call this problem the inverse metric traveling salesman problem against the minimum spanning tree algorithm and show that it is closely related to the inverse metric spanning tree problem. Keywords: Combinatorial Optimization, Inverse Optimization, TSP, Minimum Spanning Tree Algorithm * Corresponding Author, E-mail: yerimchung@yonsei.ac.kr 1. INTRODUCTION In (Chung, 2010; Chung and Demange, 2012), some variant of the inverse optimization problem is defined with respect to a specific algorithm. For a combinatorial optimization problem, we are given an instance

Quaternion-valued robust adaptive beamformer for electromagnetic vector-sensor arrays with worst-case constraint

A robust adaptive beamforming scheme based on two-component electromagnetic (EM) vector-sensor arrays is proposed by extending the well-known worst-case constraint into the quaternion domain. After defining the uncertainty set of the desired signal׳s quaternionic steering vector, two quaternion-valued constrained minimization problems are derived. We then reformulate them into two real-valued convex quadratic problems, which can be easily solved via the so-called second-order cone (SOC) programming method. It is also demonstrated that the proposed algorithms can be classified as a specific type of the diagonal loading scheme, in which the optimal loading factor is a function of the known level of uncertainty of the desired steering vector. Numerical simulations show that our new method can cope with the steering vector mismatch problem well, and alleviate the finite sample size effect to some extent. Besides, the proposed beamformer significantly outperforms the sample matrix inversion minimum variance distortionless response (SMI-MVDR) and the quaternion Capon (Q-Capon) beamformers in all the scenarios studied, and achieves a better performance than the traditional diagonal loading scheme, in the case of smaller sample sizes and higher SNRs.

Models for inverse minimum spanning tree problem with fuzzy edge weights

An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, a type of fuzzy inverse minimum spanning tree problem is introduced from a LAN reconstruction problem, where the weights of edges are assumed to be fuzzy variables. The concept of fuzzy α-minimum spanning tree is initialized, and subsequently a fuzzy α-minimum spanning tree model and a credibility maximization model are presented to formulate the problem according to different decision criteria. In order to solve the two fuzzy models, a fuzzy simulation for computing credibility is designed and then embedded into a genetic algorithm to produce some hybrid intelligent algorithms. Finally, some computational examples are given to illustrate the effectiveness of the proposed algorithms.

Note on “Inverse minimum cost flow problems under the weighted Hamming distance”

Jiang et al. proposed an algorithm to solve the inverse minimum cost flow problems under the bottleneck-type weighted Hamming distance [Y. Jiang, L. Liu, B. Wuc, E. Yao, Inverse minimum cost flow problems under the weighted Hamming distance, European Journal of Operational Research 207 (2010) 50–54]. In this note, it is shown that their proposed algorithm does not solve correctly the inverse problem in the general case due to some incorrect results in that article. Then, a new algorithm is proposed to solve the inverse problem in strongly polynomial time. The algorithm uses the linear search technique and solves a shortest path problem in each iteration.

The Partial Inverse Minimum Connected Spanning Subgraph Problem with Given Cyclomatic Number

In this paper, we consider a partial inverse problem of minimum connected spanning subgraph with cyclomatic number . That is, given a subgraph, a cyclomatic number and a constraint that the edge weights can only decrease, we want to modify the edge weights as little as possible, so that there exists a minimum connected spanning subgraph with cyclomatic number and containing the given subgraph. For the case that the given subgraph is a connected subgraph with cyclomatic number , we solve the problem in polynomial time by contracting the subgraph. And when the given subgraph is a spanning tree, we solve the problem in polynomial time by using the MST algorithm.

Some inverse optimization problems on network

In this paper, the authors consider some inverse problems on network, such as the inverse transport problems with gains (IGTP) and the inverse linear fractional minimum cost flow problem (IFFP). Firstly, the authors give the mathematics model of (IGTP) and an efficient method of solving it under l1 norm; Secondly, taking advantage of the optimality conditions, the authors consider the (IFFP) and give a simple method of solving it. Finally, an numerical example test is also developed.

Two Uncertain Programming Models for Inverse Minimum Spanning Tree Problem

An inverse minimum spanning tree problem makes the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, the concept of uncertain α-minimum spanning tree is initiated for minimum spanning tree problem with uncertain edge weights. Using different decision criteria, two uncertain programming models are presented to formulate a specific inverse minimum spanning tree problem with uncertain edge weights involving a sum-type model and a minimax-type model. By means of the operational law of independent uncertain variables, the two uncertain programming models are transformed to their equivalent deterministic models which can be solved by classic optimization methods. Finally, some numerical examples on a traffic network reconstruction problem are put forward to illustrate the effectiveness of the proposed models.

Inverse minimum cost flow problems under the weighted Hamming distance

Given a network N( V, A, u, c) and a feasible flow x 0, an inverse minimum cost flow problem is to modify the cost vector as little as possible to make x 0 form a minimum cost flow of the network. The modification can be measured by different norms. In this paper, we consider the inverse minimum cost flow problems, where the modification of the arcs is measured by the weighted Hamming distance. Both the sum-type and the bottleneck-type cases are considered. For the former, it is shown to be APX-hard due to the weighted feedback arc set problem. For the latter, we present a strongly polynomial algorithm which can be done in O( n · m 2).

SMI-MVDR Beamformer Implementations for Large Antenna Array and Small Sample Size

Two online implementations of the sample matrix inversion minimum variance distortionless response (SMI-MVDR) antenna array beamformer, based on recursive updating of the diagonal loading triangular matrix decomposition, are presented. The first proposed beamformer uses the Cholesky factorization recursive updating of the matrix whose dimension is increasing. The second beamformer uses the Householder transform (HT) recursive updating of the modified input data matrix. The proposed implementations consist primarily of vector operations, that is, they are suitable for parallel implementations with FPGAs or DSPs. The computational cost of the proposed beamforming algorithms is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nk</i> ), where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the number of antenna array elements, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> is the number of processing snapshots. The proposed implementations are especially useful for large antenna array applications, where the number of available snapshots does not exceed the number of the array antenna elements. The simulation result shows that the numerical performance of the proposed beamformers is superior, relative to the conventional recursive MVDR beamformer implementation.