Abstract
We study the competitive ratio of certain online algorithms for a well-studied class of load balancing problems. These algorithms are obtained and analyzed according to a method by Crescenzi et al (2004). We show that an exact analysis of their competitive ratio on certain “uniform” instances would resolve a fundamental conjecture by Caccetta and Häggkvist (1978). The conjecture is that any digraph on n nodes and minimum outdegree d must contain a directed cycle involving at most ⌈n/d ⌉ nodes. Our results are the first relating this conjecture to the competitive analysis of certain algorithms, thus suggesting a new approach to the conjecture itself. We also prove that, on “uniform” instances, the analysis by Crescenzi et al (2004) gives only trivial upper bounds, unless we find a counterexample to the conjecture. This is in contrast with other (notable) examples where the same analysis yields optimal (non-trivial) bounds.
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Monti, A., Penna, P., Silvestri, R. (2007). An Equivalent Version of the Caccetta-Häggkvist Conjecture in an Online Load Balancing Problem. In: Brandstädt, A., Kratsch, D., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2007. Lecture Notes in Computer Science, vol 4769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74839-7_16
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DOI: https://doi.org/10.1007/978-3-540-74839-7_16
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