Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
The Level Ancestor Problem Simplified
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Faster Swap Edge Computation in Minimum Diameter Spanning Trees
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Finding best swap edges minimizing the routing cost of a spanning tree
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Stable routing under the Spanning Tree Protocol
Operations Research Letters
Sharp bounds on Davenport-Schinzel sequences of every order
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We consider a two-edge connected, undirected graph G=(V,E), with n nodes and m non-negatively real weighted edges, and a single source shortest paths tree (SPT) T of G rooted at an arbitrary node r. If an edge in T is temporarily removed, it makes sense to reconnect the nodes disconnected from the root by adding a single non-tree edge, called a swap edge, instead of rebuilding a new optimal SPT from scratch. In the past, several optimality criteria have been considered to select a best possible swap edge. In this paper we focus on the most prominent one, that is the minimization of the average distance between the root and the disconnected nodes. To this respect, we present an O(mlog2n) time and O(m) space algorithm to find a best swap edge for every edge of T, thus improving for m=o(n2/log2n) the previously known O(n2) time and space complexity algorithm.