Cyclic games and an algorithm to find minimax cycle means in directed graphs
USSR Computational Mathematics and Mathematical Physics
The complexity of mean payoff games on graphs
Theoretical Computer Science
Theory of hybrid systems and discrete event systems
Theory of hybrid systems and discrete event systems
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Methods and Applications of (MAX, +) Linear Algebra
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
The equation A ⊗ x = B ⊗ y over (max, +)
Theoretical Computer Science
Scheduling with AND/OR Precedence Constraints
SIAM Journal on Computing
How to solve large scale deterministic games with mean payoff by policy iteration
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games
Discrete Applied Mathematics
Inferring Min and Max Invariants Using Max-Plus Polyhedra
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Approximative Methods for Monotone Systems of Min-Max-Polynomial Equations
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
The Max-Atom Problem and Its Relevance
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
An Exponential Lower Bound for the Parity Game Strategy Improvement Algorithm as We Know it
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Hard problems in max-algebra, control theory, hypergraphs and other areas
Information Processing Letters
Static analysis by policy iteration on relational domains
ESOP'07 Proceedings of the 16th European conference on Programming
The number of extreme points of tropical polyhedra
Journal of Combinatorial Theory Series A
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
A policy iteration algorithm for computing fixed points in static analysis of programs
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Precise relational invariants through strategy iteration
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
The level set method for the two-sided max-plus eigenproblem
Discrete Event Dynamic Systems
On the integer max-linear programming problem
Discrete Applied Mathematics
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Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to study the tropical analogue of the classical linear-fractional programming problem. We construct an associated parametric mean payoff game problem, and show that the optimality of a given point, or the unboundedness of the problem, can be certified by exhibiting a strategy for one of the players having certain infinitesimal properties (involving the value of the game and its derivative) that we characterize combinatorially. We use this idea to design a Newton-like algorithm to solve tropical linear-fractional programming problems, by reduction to a sequence of auxiliary mean payoff game problems.