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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alur, R., Henzinger, T.A.: Finitary fairness. ACM Trans. on Programming Languages and Systems 20(6) (1998)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
de Alfaro, L.: From fairness to chance. ENTCS 22 (2000)
Dershowitz, N., Jayasimha, D.N., Park, S.: Bounded fairness. In: Dershowitz, N. (ed.) Verification: Theory and Practice. LNCS, vol. 2772, pp. 304–317. Springer, Heidelberg (2003)
Francez, N.: Fairness. Springer, Heidelberg (1986)
Kwiatkowska, M.: Survey of fairness notions. Information and Software Technology 31(7), 371–386 (1989)
Lehmann, D., Pnueli, A., Stavi, J.: Impartiality, justice and fairness: The ethics of concurrent termination. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 264–277. Springer, Heidelberg (1981)
Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer, Heidelberg (1991)
Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley-Interscience, Hoboken (1988)
Parikh, R.J.: On Context-Free Languages. Journal of the ACM 13(4), 570–581 (1966)
Wikipedia. Crop rotation (2009), http://www.wikipedia.com
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-03816-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03815-0
Online ISBN: 978-3-642-03816-7
eBook Packages: Computer ScienceComputer Science (R0)