Theoretical Computer Science - Special issue on dynamic and on-line algorithms
On-line load balancing of temporary tasks
Journal of Algorithms
Directed triangles in digraphs
Journal of Combinatorial Theory Series B
On-Line Load Balancing in a Hierarchical Server Topology
SIAM Journal on Computing
Developments from a June 1996 seminar on Online algorithms: the state of the art
On-line load balancing made simple: Greedy strikes back
Journal of Discrete Algorithms
A self-repairing peer-to-peer system resilient to dynamic adversarial churn
IPTPS'05 Proceedings of the 4th international conference on Peer-to-Peer Systems
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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.