In this paper we introduce integer quadratic programming (IQP) approach to detect QPSK Code Spread OFDM (CSOFDM) signal by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) alg...
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ISBN:
(纸本)9781467350501
In this paper we introduce integer quadratic programming (IQP) approach to detect QPSK Code Spread OFDM (CSOFDM) signal by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose preprocessing procedures that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The basic idea of the proposed preprocessing is to introduce a good choice of upper bound for the BB search tree and/or reduce the search space of the BB problem. Performance and complexity computations of these preprocessing are investigated. Simulation results show that the proposed preprocessing when applied prior to BB provides optimal or near optimal performance with a significantly reduced computational complexity.
We study in this paper a general case of integerquadratic multi-knapsack problem (QMKP) where the objective function is non separable. An upper bound is proposed for (QMKP) which is computed via two steps. We first r...
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We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice Zn. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optima...
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We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice Zn. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the problem. By interpreting the solution to the SDP relaxation probabilistically, we obtain a randomized algorithm for finding good suboptimal solutions, and thus an upper bound on the optimal value. The effectiveness of the method is shown for numerical problem instances of various sizes.
作者:
KORNER, FSektion Mathematik
Technische Universität Dresden Mommsenstrasse 13 DDR-8027 Dresden German Democratic Republic
The quadraticintegerprogramming problem is considered. It will be shown in which order the variablesx1, ...,x n should be ramified in order to reduce the number of knots being studied to a minimum. There areO(n3) op...
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The quadraticintegerprogramming problem is considered. It will be shown in which order the variablesx1, ...,x n should be ramified in order to reduce the number of knots being studied to a minimum. There areO(n3) operations necessary to determine a favourable ramification. Numerical tests confirm the efficiency of the given algorithm.
A minimum sum vertex cover of an n-vertex graph G is a bijection : V(G)->[] that minimizes the cost ex) min ($(u). $()). Finding a minimum sum vertex cover of a graph (the MSVC problem) is NP-hard. MSVC is studied ...
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A minimum sum vertex cover of an n-vertex graph G is a bijection : V(G)->[] that minimizes the cost ex) min ($(u). $()). Finding a minimum sum vertex cover of a graph (the MSVC problem) is NP-hard. MSVC is studied well in the realm of approximation algorithms. The best- known approximation factor in polynomial time for the problem is 16/9 [Bansal, Batra, Farhadi, and Tetali, SODA 2021]. Recently, Stankovic [APPROX/RANDOM 2022) proved that achieving an approximation ratio better than 1.014 for MSVC is NP-hard, assuming the Unique Games Conjecture. We study the MSVC problem from the perspective of parameterized algorithms. The parameters consider are the size of a minimum vertex cover and the size of a minimum clique modulator of the input graph. We obtain the following results. MSVC can be solved in 2000) time, where k is the size of a minimum vertex cover. MSVC can be solved in (k) time for some computable function, where k is the size of a minimum clique modulator.
Pose graph optimization from relative measurements is challenging because of the angular component of the poses: the variables live on a manifold product with nontrivial topology and the likelihood function is nonconv...
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Pose graph optimization from relative measurements is challenging because of the angular component of the poses: the variables live on a manifold product with nontrivial topology and the likelihood function is nonconvex and has many local minima. Because of these issues, iterative solvers are not robust to large amounts of noise. This paper describes a global estimation method, called multi-hypothesis orientation-from-lattice estimation in 2-D (MOLE2D), for the estimation of the nodes' orientation in a pose graph. We demonstrate that the original nonlinear optimization problem on the manifold product is equivalent to an unconstrained quadratic optimization problem on the integer lattice. Exploiting this insight, we show that, in general, the maximum likelihood estimate alone cannot be considered a reliable estimator. Therefore, MOLE2D returns a set of point estimates, for which we can derive precise probabilistic guarantees. Experiments show that the method is able to tolerate extreme amounts of noise, far above all noise levels of sensors used in applications. Using MOLE2D's output to bootstrap the initial guess of iterative pose graph optimization methods improves their robustness and makes them avoid local minima even for high levels of noise.
Feature matching problem that incorporates pair-wise constraints can be formulated as an integer quadratic programming (IQP) problem with one-to-one matching constraint. Since it is NP-hard, relaxation models are requ...
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Feature matching problem that incorporates pair-wise constraints can be formulated as an integer quadratic programming (IQP) problem with one-to-one matching constraint. Since it is NP-hard, relaxation models are required. One main challenge for optimizing IQP matching is how to incorporate the discrete one-to-one matching constraint in IQP matching optimization. In this paper, we present a new feature matching relaxation model, called Nonnegative Orthogonal Relaxation (NOR), that aims to optimize IQP matching problem in nonnegative orthogonal domain. One important benefit of the proposed NOR model is that it can naturally incorporate the discrete one-to-one matching constraint in its optimization and can return a desired sparse (approximate discrete) solution for the problem. An efficient and effective update algorithm has been developed to solve the proposed NOR model. Promising experimental results on several benchmark datasets demonstrate the effectiveness and efficiency of the proposed NOR method.
We present a new method of obtaining lower bounds for a class of quadratic 0, 1 programs that includes the quadratic assignment problem. The method generates a monotonic sequence of lower bounds and may be interpreted...
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We present a new method of obtaining lower bounds for a class of quadratic 0, 1 programs that includes the quadratic assignment problem. The method generates a monotonic sequence of lower bounds and may be interpreted as a Lagrangean dual ascent procedure. We report on a computational comparison of our bounds with earlier work in [2] based on subgradient techniques.
Barahona described a linear time algorithm for a class of 0-1 quadraticprogramming problems. The algorithm was based on a transformation to a max-cut problem. We describe a linear algorithm that treats a slightly mor...
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Barahona described a linear time algorithm for a class of 0-1 quadraticprogramming problems. The algorithm was based on a transformation to a max-cut problem. We describe a linear algorithm that treats a slightly more general problem directly in its original form. We then give a pseudopolynomial algorithm for even more general problems.
Rooted trees are ubiquitous data structures which are used to model hierarchical objects from a plethora of different application domains. For various downstream analysis tasks, measures are needed that quan-tify (dis...
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Rooted trees are ubiquitous data structures which are used to model hierarchical objects from a plethora of different application domains. For various downstream analysis tasks, measures are needed that quan-tify (dis-)similarity between rooted trees. Many such measures exist, e. g., the widely used tree edit dis-tance (TED). However, there are few algorithms to compute (dis-)similarity measures which are specifi-cally designed for rooted, unordered, node-labeled trees and support input trees of different orders. To close this gap in the literature, we introduce the edge-preservation similarity (EPS). We show how to exactly compute EPS via integer quadratic programming on small instances and present a scalable 4-approximation algorithm. An evaluation on tree representations of pseudoknotted RNA secondary struc-tures and acyclic molecular graphs shows that both exact and approximate (normalized) EPS better preserves functional similarities between the compared RNAs and molecules than the often-used TED. Python implementations of our algorithms and scripts to reproduce the results are available on GitHub: https://***/bionetslab/edge-preservation-similarity . (c) 2023 Elsevier B.V. All rights reserved.
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