Competitive algorithms for on-line problems
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On the power of randomization in online algorithms
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Telecommunications network design algorithms
Telecommunications network design algorithms
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A polynomial time approximation scheme for minimum routing cost spanning trees
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Deterministic Polylog Approximation for Minimum Communication Spanning Trees
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Self-Stabilizing Distributed Queuing
IEEE Transactions on Parallel and Distributed Systems
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This paper considers an enhancement to the arrow distributed directory protocol, introduced in [8]. The arrow protocol implements a directory service, allowing nodes to locate mobile objects in a distributed system, while ensuring mutual exclusion in the presence of concurrent requests. The arrow protocol makes use of a minimum spanning tree (MST) Tm of the network, selected during system initialization, resulting in a worst-case overhead ratio of (1 + stretch(Tm))/2. However, we observe that the arrow protocol is correct communicating over any spanning tree T of G. We show that the worst-case overhead ratio is minimized by the minimum stretch spanning tree (MSST), and that the problem cannot be approximated within a factor better than (1 +√5)/2, unless P = NP. In contrast, other trees may be more suitable if one is interested in the average-case behavior of the network. We show that in the case where the distribution of the requests is fixed and known in advance, the expected communication is minimized using the minimum communication cost spanning tree (MCT). It is shown that the resulting MCT problem is a restricted case for which one can find a tree T over which the expected communication cost of the arrow protocol is at most 1:5 times the expected communication cost of an optimal protocol. We also show that even if the distribution of the requests is not fixed, or not known to the algorithm in advance, then if the adversary is oblivious, one may use probabilistic approximation of metric spaces [2,3] to ensure an expected overhead ratio of O(log n log log n) in general, and an expected overhead ratio of O(log n) in the case of constant dimension Euclidean graphs.