How to Swap a Failing Edge of a Single Source Shortest Paths Tree
نویسندگان
چکیده
In this paper we introduce the notion of best swap for a failing edge of a single source shortest paths tree (SPT) S(r) rooted in r in a weighted graph G = (V, E). Given an edge e ∈ S(r), an edge e′ ∈ E \{e} is a swap edge if the swap tree Se/e′(r) obtained by swapping e with e′ in S(r) is a spanning tree of G. A best swap edge for a given edge e is a swap edge minimizing some distance functional between r and the set of nodes disconnected from the root after the edge e is removed. A swap algorithm with respect to some distance functional computes a best swap edge for every edge in S(r). We show that there exist fast swap algorithms (much faster than recomputing from scratch a new SPT) which also preserve the functionality of the affected SPT.
منابع مشابه
Swapping a Failing Edge of a Shortest Paths Tree by Minimizing the Average Stretch Factor
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...
متن کاملEffective Edge-Fault-Tolerant Single-Source Spanners via Best (or Good) Swap Edges
Computing all best swap edges (ABSE) of a spanning tree T of a given n-vertex and m-edge undirected and weighted graph G means to select, for each edge e of T , a corresponding non-tree edge f , in such a way that the tree obtained by replacing e with f enjoys some optimality criterion (which is naturally defined according to some objective function originally addressed by T ). Solving efficien...
متن کاملDistributed Computation for Swapping a Failing Edge
We consider the problem of computing the best swap edges of a shortest-path tree Tr rooted in r. That is, given a single link failure: if the path is not affected by the failed link, then the message will be delivered through that path; otherwise, we want to guarantee that, when the message reaches the edge (u, v) where the failure has occurred, the message will then be re-routed using the comp...
متن کاملSemi-Dynamic Shortest Paths and Breadth-First Search in Digraphs
In this paper we study the problem of maintaining a single source shortest path tree or a breadth-rst search tree for a directed graph, in either an incremental or decremental setting. We maintain a single source shortest path tree of a directed graph G with unit edge weights during a sequence of edge deletions in total time O(mn), thus obtaining a O(n) amortized time for each deletion if the s...
متن کاملI/O-Efficient Undirected Shortest Paths with Unbounded Edge Lengths
We show how to compute single-source shortest paths in undirected graphs with non-negative edge lengths in O( p nm/B logn+ MST (n, m)) I/Os, where n is the number of vertices, m is the number of edges, B is the disk block size, and MST (n, m) is the I/O-cost of computing a minimum spanning tree. For sparse graphs, the new algorithm performs O((n/ √ B) logn) I/Os. This result removes our previou...
متن کامل