Amortized efficiency of list update and paging rules
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
New results on the old k-opt algorithm for the TSP
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Dynamic session management for static and mobile users: a competitive on-line algorithmic approach
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
New results for online page replication
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Competitive distributed file allocation
Information and Computation
New results for online page replication
Theoretical Computer Science - Special issue: Online algorithms in memoriam, Steve Seiden
Universal approximations for TSP, Steiner tree, and set cover
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Improved lower and upper bounds for universal TSP in planar metrics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
GIST: group-independent spanning tree for data aggregation in dense sensor networks
DCOSS'06 Proceedings of the Second IEEE international conference on Distributed Computing in Sensor Systems
Efficient multicast trees with local knowledge on wireless ad hoc networks
WWIC'05 Proceedings of the Third international conference on Wired/Wireless Internet Communications
Theoretical Computer Science
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Suppose we are given a sequence of n points v1,…,vn in the Euclidean plane, and our objective is to construct, on-line, a connected graph that connects all of them, trying to minimize the total sum of lengths of its edges. We assume that the points appear one at a time, vi arriving at step i. At the end of step i, the on-line algorithm must construct a connected graph Ti-1. This can be done by joining vi (not necessarily by a straight line) to any point of Ti-1, which need not necessarily be one of the previously given points vj. The performance of our algorithm is measured by its competitive ratio: the supremum, over all sequences v1,…,vn as above, of the ratio between the total length of the graph constructed by our algorithm and the total length of the best Steiner tree that connects all the points v1,…, vn. There are known on-line algorithms whose competitive ratio is O(log n), but there is no known nontrivial lower bound for the best possible competitive ratio. Here we prove that the upper bound is almost tight by establishing an &OHgr;(log n/log log n) lower bound for the competitive ratio of any on-line algorithm. The lower bound holds for deterministic algorithms as well as for randomized ones, and obviously holds in any Euclidean space of dimension greater than 2 as well.