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
A Polynomial-Time Approximation Scheme for Minimum Routing Cost Spanning Trees
SIAM Journal on Computing
Approximation algorithms for some optimum communication spanning tree problems
Discrete Applied Mathematics
Point-of-Failure Shortest-Path Rerouting: Computing the Optimal Swap Edges Distributively
IEICE - Transactions on Information and Systems
Swapping a failing edge of a shortest paths tree by minimizing the average stretch factor
Theoretical Computer Science
The Swap Edges of a Multiple-Sources Routing Tree
Algorithmica
Faster Swap Edge Computation in Minimum Diameter Spanning Trees
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Computing Best Swaps in Optimal Tree Spanners
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Improved bounds and new techniques for Davenport--Schinzel sequences and their generalizations
Journal of the ACM (JACM)
Sensitivity analysis of minimum spanning trees in sub-inverse-ackermann time
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A distributed algorithm for finding all best swap edges of a minimum diameter spanning tree
DISC'07 Proceedings of the 21st international conference on Distributed Computing
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Given an n-node, undirected and 2-edge-connected graph G = (V,E) with positive real weights on its m edges, given a set of k source nodes S ⊆ V, and given a spanning tree T of G, the routing cost of T w.r.t. S is the sum of the distances in T from every source s ∈ S to all the other nodes of G. If an edge e of T undergoes a transient failure and connectivity needs to be promptly reestablished, then to reduce set-up and rerouting costs it makes sense to temporarily replace e by means of a swap edge, i.e., an edge in G reconnecting the two subtrees of T induced by the removal of e. Then, a best swap edge for e is a swap edge which minimizes the routing cost of the tree obtained after the swapping. As a natural extension, the all-best swap edges problem is that of finding a best swap edge for every edge of T. Such a problem has been recently solved in O(mn) time and linear space for arbitrary k, and in O(n2 +m log n) time and O(n2) space for the special case k = 2. In this paper, we are interested to the prominent cases k = O(1) and k = n, which model realistic communication paradigms. For these cases, we present a linear space and Õ(m) time algorithm, and thus we improve both the above running times (but for quite dense graphs in the case k = 2, for which however it is noticeable we make use of only linear space). Moreover, we provide an accurate analysis showing that when k = n, the obtained swap tree is effective in terms of routing cost.