Fast Algorithms for Monotonic Discounted Linear Programs with Two Variables per Inequality∗
نویسندگان
چکیده
We suggest new strongly polynomial algorithms for solving linear programs min( ∑ xi|S) with constraints S of the monotonic discounted form xi ≥ λxj + β with 0 < λ < 1. The algorithm for the case when the discounting factor λ is equal for all constraints is O(mn2), whereas the algorithm for the case when λ may vary between the constraints is O(mn2 logm), where n is the number of variables and m is the number of constraints. As applications, we obtain the best currently available algorithm for two-player discounted payoff games and a new faster strongly subexponential algorithm for the ergodic partition problem for mean payoff games.
منابع مشابه
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
The authors present an O(inn log m) algorithm for solving feasibility in linear programs with up to two variables per inequality which is derived directly from the Fourier-Motzkin elimination method. (The number of variables and inequalities are denoted by n and m, respectively.) The running time of the algorithm dominates that of the best known algorithm for the problem, and is far simpler. In...
متن کاملSome Results on facets for linear inequality in 0-1 variables
The facet of Knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. Such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. Strong covers for facets of Knapsack ploytope has been developed in the first pa...
متن کاملTight bounds and 2-approximation algorithms for integer programs with two variables per inequality
The problem of integer programming in bounded variables, over constraints with no more than two variables in each constraint is NP-complete, even when all variables are binary. This paper deals with integer linear minimization problems in n variables subject to m linear constraints with at most two variables per inequality, and with all variables bounded between 0 and U. For such systems, a 2?a...
متن کاملConcise algorithm for linear programs in matlab: monotonic convergence, basic variables, boundedness
A physically concise polynomial-time iterative algorithm due to Barnes – a variation of Karmarkar projective transformation algorithm – is presented in Matlab for linear programs 0 , x b Ax to subject x c Min t . The concerned monotonic convergence of the solution vector and the consequent detection of basic variables are stated. The boundedness of the solution, multiple solutions, and no s...
متن کاملLinear programming on SS-fuzzy inequality constrained problems
In this paper, a linear optimization problem is investigated whose constraints are defined with fuzzy relational inequality. These constraints are formed as the intersection of two inequality fuzzy systems and Schweizer-Sklar family of t-norms. Schweizer-Sklar family of t-norms is a parametric family of continuous t-norms, which covers the whole spectrum of t-norms when the parameter is changed...
متن کامل