Theory of linear and integer programming
Theory of linear and integer programming
Fairness
Integer and combinatorial optimization
Integer and combinatorial optimization
Information and Software Technology
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
ACM Transactions on Programming Languages and Systems (TOPLAS)
Journal of the ACM (JACM)
Information and Computation - Special issue on FLOC '96
Operating Systems Theory
Introduction to Algorithms
Impartiality, Justice and Fairness: The Ethics of Concurrent Termination
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Balanced Paths in Colored Graphs
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Half-Positional determinacy of infinite games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Finitary winning in ω-regular games
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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We consider finite graphs whose edges are labeled with elements, called colors, taken from a fixed finite alphabet. We study the problem of determining whether there is an infinite path where either (i) all colors occur with a fixed asymptotic frequency, or (ii) there is a constant that bounds the difference between the occurrences of any two colors for all prefixes of the path. These properties can be viewed as quantitative refinements of the classical notion of fair path in a concurrent system, whose simplest form checks whether all colors occur infinitely often. Our notions provide stronger criteria, particularly suitable for scheduling applications based on a coarse-grained model of the jobs involved. In particular, they enforce a given set of priorities among the jobs involved in the system. We show that both problems we address are solvable in polynomial time, by reducing them to the feasibility of a linear program. We also consider two-player games played on finite colored graphs where the goal is one of the above frequency-related properties. For all the goals, we show that the problem of checking whether there exists a winning strategy is Co-NP-complete.