Approximating the spectral radius of sets of matrices in the max-algebra is NP-hard

2000 ◽  
Vol 45 (9) ◽  
pp. 1762-1765 ◽  
Author(s):  
V.D. Blondel ◽  
S. Gaubert ◽  
J.N. Tsitsiklis
Keyword(s):  
Spectral Radius ◽  
Np Hard ◽  
Max Algebra

scholarly journals Generalized spectral radius and its max algebra version

2013 ◽  
Vol 439 (4) ◽  
pp. 1006-1016 ◽  
Author(s):  
Vladimir Müller ◽  
Aljoša Peperko
Keyword(s):  
Spectral Radius ◽  
Max Algebra ◽  
Generalized Spectral Radius

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

SPECTRAL RADIUS OF NONSINGULAR TRANSFORMATIONS

1989 ◽  
Vol 15 (1) ◽  
pp. 275
Author(s):  
NADKARNI ◽  
ROBERTSON
Keyword(s):  
Spectral Radius

scholarly journals Optimizing Transmit Sequence and Instrumental Variables Receiver for Dual-Function Complexity System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yu Yao ◽  
Junhui Zhao ◽  
Lenan Wu
Keyword(s):  
Approximate Solution ◽  
Instrumental Variables ◽  
Performance Index ◽  
Dual Function ◽  
Np Hard ◽  
Match Filter ◽  
Filter Output ◽  
Phase Code ◽  
Discrete Phase ◽  
Simulation Results

This correspondence deals with the joint cognitive design of transmit coded sequences and instrumental variables (IV) receive filter to enhance the performance of a dual-function radar-communication (DFRC) system in the presence of clutter disturbance. The IV receiver can reject clutter more efficiently than the match filter. The signal-to-clutter-and-noise ratio (SCNR) of the IV filter output is viewed as the performance index of the complexity system. We focus on phase only sequences, sharing both a continuous and a discrete phase code and develop optimization algorithms to achieve reasonable pairs of transmit coded sequences and IV receiver that fine approximate the behavior of the optimum SCNR. All iterations involve the solution of NP-hard quadratic fractional problems. The relaxation plus randomization technique is used to find an approximate solution. The complexity, corresponding to the operation of the proposed algorithms, depends on the number of acceptable iterations along with on and the complexity involved in all iterations. Simulation results are offered to evaluate the performance generated by the proposed scheme.

scholarly journals On Gibbs Measures and Spectra of Ruelle Transfer Operators

2017 ◽  
Vol 60 (2) ◽  
pp. 411-421
Author(s):  
Luchezar Stoyanov
Keyword(s):  
Spectral Radius ◽  
Spectral Properties ◽  
Gibbs Measures ◽  
Transfer Operator ◽  
Frobenius Theorem ◽  
Transfer Operators

AbstractWe prove a comprehensive version of the Ruelle–Perron–Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the Hölder constant of the function generating the operator appears only polynomially, not exponentially as in previously known estimates.

On the Complexity of Deadlock Recovery

1986 ◽  
Vol 9 (3) ◽  
pp. 323-342
Author(s):  
Joseph Y.-T. Leung ◽  
Burkhard Monien
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Arbitrary Number ◽  
The Other ◽  
Np Hard ◽  
Total Cost ◽  
Other Hand ◽  
Input Parameters ◽  
Resource Type

We consider the computational complexity of finding an optimal deadlock recovery. It is known that for an arbitrary number of resource types the problem is NP-hard even when the total cost of deadlocked jobs and the total number of resource units are “small” relative to the number of deadlocked jobs. It is also known that for one resource type the problem is NP-hard when the total cost of deadlocked jobs and the total number of resource units are “large” relative to the number of deadlocked jobs. In this paper we show that for one resource type the problem is solvable in polynomial time when the total cost of deadlocked jobs or the total number of resource units is “small” relative to the number of deadlocked jobs. For fixed m ⩾ 2 resource types, we show that the problem is solvable in polynomial time when the total number of resource units is “small” relative to the number of deadlocked jobs. On the other hand, when the total number of resource units is “large”, the problem becomes NP-hard even when the total cost of deadlocked jobs is “small” relative to the number of deadlocked jobs. The results in the paper, together with previous known ones, give a complete delineation of the complexity of this problem under various assumptions of the input parameters.

scholarly journals Using Machine Learning for Quantum Annealing Accuracy Prediction

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 187
Author(s):  
Aaron Barbosa ◽  
Elijah Pelofske ◽  
Georg Hahn ◽  
Hristo N. Djidjev
Keyword(s):  
Machine Learning ◽  
Maximum Clique ◽  
Classification Model ◽  
Maximum Clique Problem ◽  
Problem Instance ◽  
Np Hard ◽  
Machine Learning Classification ◽  
Hard Problems ◽  
Problem Instances ◽  
D Wave

Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters, such as the D-Wave’s chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem will be solvable to optimality with the D-Wave 2000Q. We extend these results by training a machine learning regression model that predicts the clique size found by D-Wave.

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