Worst-case Analysis of Set Union Algorithms
Journal of the ACM (JACM)
Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Efficient algorithms for finding the most vital edge of a minimum spanning tree
Information Processing Letters
Finding the detour-critical edge of a shortest path between two nodes
Information Processing Letters
Maintaining Spanning Trees of Small Diameter
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Minimizing Diameters of Dynamic Trees
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Dynamic Maintenance Versus Swapping: An Experimental Study on Shortest Paths Trees
WAE '00 Proceedings of the 4th International Workshop on Algorithm Engineering
Maintaining a Minimum Spanning Tree Under Transient Node Failures
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
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In network communication systems, frequently messages are routed along a minimum diameter spanning tree (MDST) of the network, to minimize the maximum delay in delivering a message. When a transient edge failure occurs, it is important to choose a temporary replacement edge which minimizes the diameter of the new spanning tree. Such an optimal replacement is called the best swap. As a natural extension, the all-best-swaps (ABS) problem is the problem of finding the best swap for every edge of the MDST. Given a weighted graph G = (V,E), where |V| = n and |E| = m, we solve the ABS problem in O(n√m) time and O(m + n) space, thus improving previous bounds for m = o(n2).