Abstract
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 the same asymptotic frequency, or (ii) there is a constant which bounds the difference between the occurrences of any two colors for all prefixes of the path. These two notions can be viewed as refinements of the classical notion of fair path, 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. We show that both problems are solvable in polynomial time, by reducing them to the feasibility of a linear program.
Work partially supported by MIUR PRIN Project 2007-9E5KM8.
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Bianco, A., Faella, M., Mogavero, F., Murano, A. (2009). Balanced Paths in Colored Graphs. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_14
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DOI: https://doi.org/10.1007/978-3-642-03816-7_14
Publisher Name: Springer, Berlin, Heidelberg
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