A strongly polynomial algorithm for solving two-sided linear systems in max-algebra
نویسندگان
چکیده
منابع مشابه
A strongly polynomial algorithm for solving two-sided linear systems in max-algebra
An algorithm for solving m× n systems of (max,+)-linear equations is presented. The systems have variables on both sides of the equations. After O(m4n4) iterations the algorithm either finds a solution of the system or finds out that no solution exists. Each iteration needs O(mn) operations so that the complexity of the presented algorithm is O(m5n5). © 2005 Elsevier B.V. All rights reserved.
متن کاملExponential behaviour of the Butkovic-Zimmermann algorithm for solving two-sided linear systems in max-algebra
In [Butkovič and Zimmermann(2006)] an ingenious algorithm for solving systems of twosided linear equations in max-algebra was given and claimed to be strongly polynomial. However, in this note we give a sequence of examples showing exponential behaviour of the algorithm. We conclude that the problem of finding a strongly polynomial algorithm is still open.
متن کاملSolving Systems of Two-Sided (Max, Min)-Linear Equations
A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.
متن کاملPolynomial Systems Solving by Fast Linear Algebra
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to stick to the most general case, we consider a representation of the solutions from which one can easily recover the exact solutions or a certified approximatio...
متن کاملA Strongly Polynomial Method for Solving Integer Max-Linear Optimization Problems in a Generic Case
We study the existence of integer solutions to max-linear optimization problems. Specifically, we show that, in a generic case, the integer max-linear optimization problem can be solved in strongly polynomial time. This extends results from our previous papers where polynomial methods for this generic case were given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2006
ISSN: 0166-218X
DOI: 10.1016/j.dam.2005.09.008