A better lower bound on the competitive ratio of the randomized 2-server problem
Information Processing Letters
Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
Online computation and competitive analysis
Online computation and competitive analysis
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
Minimum-energy broadcasting in static ad hoc wireless networks
Wireless Networks
Maintaining Minimum Spanning Trees in Dynamic Graphs
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Parametric and Kinetic Minimum Spanning Trees
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Data structures for on-line updating of minimum spanning trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
ALMI: an application level multicast infrastructure
USITS'01 Proceedings of the 3rd conference on USENIX Symposium on Internet Technologies and Systems - Volume 3
The power of recourse for online MST and TSP
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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We consider the problem of maintaining a minimum spanning tree within a graph with dynamically changing edge weights. An online algorithm is confronted with an input sequence of edge weight changes and has to choose a minimum spanning tree after each such change in the graph. The task of the algorithm is to perform as few changes in its minimum spanning tree as possible.We compare the number of changes in the minimum spanning tree produced by an online algorithm and that produced by an optimal offline algorithm. The number of changes is counted in the number of edges changed between spanning trees in consecutive rounds.For any graph with nvertices we provide a deterministic algorithm achieving a competitive ratio of $\mathcal{O}(n^2)$. We show that this result is optimal up to a constant. Furthermore we give a lower bound for randomized algorithms of 茂戮驴(logn). We show a randomized algorithm achieving a competitive ratio of $\mathcal{O}(n\log n)$ for general graphs and $\mathcal{O}(\log n)$ for planar graphs.