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Finding All the Best Swaps of a Minimum Diameter Spanning Tree Under Transient Edge Failures
 Journal of Graph Algorithms and Applications
, 1998
"... Abstract. 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 ..."
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Cited by 14 (6 self)
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Abstract. 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 allbestswaps (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,wesolvetheABSprobleminO(n √ m)time and O(m + n) space, thus improving previous bounds for m = o(n 2). 1
Computing all the best swap edges distributively
 PROC. 8TH INT. CONFERENCE ON PRINCIPLES OF DISTRIBUTED SYSTEMS (OPODIS’04), LNCS 3544
, 2004
"... Recently great attention has been given to pointoffailure swap rerouting, an efficient technique for routing in presence of transient failures. According to this technique, a message follows the normal routing table information unless the next hop has failed; in this case, it is redirected towards ..."
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Cited by 6 (4 self)
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Recently great attention has been given to pointoffailure swap rerouting, an efficient technique for routing in presence of transient failures. According to this technique, a message follows the normal routing table information unless the next hop has failed; in this case, it is redirected towards a precomputed link, called swap; once this link has been crossed, normal routing is resumed. The amount of precomputed information required in addition to the routing table is rather small: a single link per each destination. Several efficient serial algorithms have been presented to compute this information; none of them can unfortunately be efficiently implemented in a distributed environment. In this paper we present protocols, based on a new strategy, that allow the efficient computation of all the optimal swap edges under several optimization criteria.
Efficient protocols for computing optimal swap edges
 In Proc. of 3rd IFIP International Conference on Theoretical Computer Science (TCS
"... Abstract We consider the problem of computing the optimal swap edges of a shortestpath tree. This theoretical problem arises in practice in systems that offer pointoffailure shortestpath rerouting service in presence of a single link failure: if the shortest path is not affected by the failed lin ..."
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Cited by 4 (4 self)
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Abstract We consider the problem of computing the optimal swap edges of a shortestpath tree. This theoretical problem arises in practice in systems that offer pointoffailure shortestpath rerouting service in presence of a single link failure: if the shortest path is not affected by the failed link, then the message will be delivered through that path; otherwise, the system will guarantee that, when the message reaches the node where the failure has occurred, the message will then be rerouted through the shortestpath to its destination. There exist highly efficient serial solutions for the problem, but unfortunately because of the structures they use, there is no known (nor foreseeable) efficient distributed implementation for them. A distributed protocol exists only for finding swap edges, not necessarily optimal ones. We present two simple and efficient distributed algorithms for computing the optimal swap edges of a shortestpath tree. One algorithm uses messages containing a constant amount of information, while the other is tailored for systems that allow long messages. The amount of data transferred by the protocols is the same and depends on on the structure of the shortestpath spanningtree; it is no more, and sometimes significantly less, than the cost of constructing the shortestpath tree.
A Distributed Algorithm for Finding All Best Swap Edges of a Minimum Diameter Spanning Tree
 IEEE TRANSACTIONS ON DEPENDABLE AND SECURE COMPUTING
, 2007
"... Communication in networks suffers if a link fails. When the links are edges of a tree that has been chosen from an underlying graph of all possible links, a broken link even disconnects the network. Most often, the link is restored rapidly. A good policy to deal with this sort of transient link fail ..."
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Cited by 3 (2 self)
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Communication in networks suffers if a link fails. When the links are edges of a tree that has been chosen from an underlying graph of all possible links, a broken link even disconnects the network. Most often, the link is restored rapidly. A good policy to deal with this sort of transient link failures is swap rerouting, where the temporarily broken link is replaced by a single swap link from the underlying graph. A rapid replacement of a broken link by a swap link is only possible if all swap links have been precomputed. The selection of high quality swap links is essential; it must follow the same objective as the originally chosen communication subnetwork. We are interested in a minimum diameter tree in a graph with edge weights (so as to minimize the maximum travel time of messages). Hence, each swap link must minimize (among all possible swaps) the diameter of the tree that results from swapping. We propose a distributed algorithm that efficiently computes all of these swap links, and we explain how to route messages across swap edges with a compact routing scheme. Finally, we consider the computation of swap edges in an arbitrary spanning tree, where swap edges are chosen to minimize the time required to adapt routing in case of a failure, and give efficient distributed algorithms for two variants of this problem.
Maintaining a minimum spanning tree under transient node failures
 Proc. of the 8th European Symposium on Algorithms (ESA 2000
"... Abstract. Given a 2node connected, undirected graph G = (V,E), with n nodes and m edges with real weights, and given a minimum spanning tree (MST) T =(V, ET)ofG, we studythe problem of finding, for everynode v ∈ V,theMSTofG − v =(V \{v},E \ Ev), where Ev is the set of edges incident to v in G. We s ..."
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Cited by 1 (1 self)
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Abstract. Given a 2node connected, undirected graph G = (V,E), with n nodes and m edges with real weights, and given a minimum spanning tree (MST) T =(V, ET)ofG, we studythe problem of finding, for everynode v ∈ V,theMSTofG − v =(V \{v},E \ Ev), where Ev is the set of edges incident to v in G. We show that this problem can be solved in O(min(m · α(n, n),m+ n log n)) time and O(m) space. Our solution improves on the previouslyknown O(m log n) time bound. 1
Brief Annoucement: Distributed Swap Edges Computation for Minimum Routing Cost Spanning Trees
"... Given a weighted graph G(VG,EG) representing a communication network, with n nodes and m edges where the weights are positive integers, its Spanning Tree is typically used to route messages. In [1] the routing cost of a spanning tree is defined as the sum of the distances over all pairs of vertices ..."
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Cited by 1 (1 self)
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Given a weighted graph G(VG,EG) representing a communication network, with n nodes and m edges where the weights are positive integers, its Spanning Tree is typically used to route messages. In [1] the routing cost of a spanning tree is defined as the sum of the distances over all pairs of vertices of this tree. Hence,
A Theory and Algorithms for Combinatorial reoptimization
"... Many reallife applications involve systems that change dynamically over time. Thus, throughout the continuous operation of such a system, it is required to compute solutions for new problem instances, derived from previous instances. Since the transition from one solution to another incurs some co ..."
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Cited by 1 (0 self)
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Many reallife applications involve systems that change dynamically over time. Thus, throughout the continuous operation of such a system, it is required to compute solutions for new problem instances, derived from previous instances. Since the transition from one solution to another incurs some cost, a natural goal is to have the solution for the new instance close to the original one (under a certain distance measure). In this paper we develop a general model for combinatorial reoptimization, encompassing classical objective functions as well as the goal of minimizing the transition cost from one solution to the other. Formally, we say that A is an (r, ρ)reapproximation algorithm if it achieves a ρapproximation for the optimization problem, while paying a transition cost that is at most r times the minimum required for solving the problem optimally. When ρ = 1 we get an (r, 1)reoptimization algorithm. Using our model we derive reoptimization and reapproximation algorithms for several important classes of optimization problems. This includes fully polynomial time reapproximation schemes for DPbenevolent problems, a class introduced by Woeginger (Proc. Tenth ACMSIAM Symposium on Discrete Algorithms, 1999), reapproximation algorithms for metric Facility Location problems, and (1, 1)reoptimization algorithm for polynomially solvable subsetselection problems. Thus, we distinguish here for the first time between classes of reoptimization problems, by their hardness status with respect to minimizing transition costs while guaranteeing a good approximation for the underlying optimization problem.
PointofFailure Swap Rerouting: Computing The Optimal Swaps Distributively
"... We consider the problem of computing the optimal swap edges of a shortestpath tree. This problem arises in designing systems that offer pointoffailure shortestpath rerouting service in presence of a single link failure: if the shortest path is not affected by the failed link, then the message wi ..."
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We consider the problem of computing the optimal swap edges of a shortestpath tree. This problem arises in designing systems that offer pointoffailure shortestpath rerouting service in presence of a single link failure: if the shortest path is not affected by the failed link, then the message will be delivered through that path; otherwise, the system will guarantee that, when the message reaches the node where the failure has occurred, the message will then be rerouted through the shortestpath to its destination. There exist highly efficient serial solutions for the problem, but unfortunately because of the structures they use, there is no known (nor foreseeable) efficient distributed implementation for them. A distributed protocol exists only for finding swap edges, not necessarily optimal ones. We present two simple and efficient distributed algorithms for computing the optimal swap edges of a shortestpath tree. One algorithm uses messages containing a constant amount of information, while the other is tailored for systems that allow long messages. The amount of data transferred by the protocols is the same and depends on the structure of the shortestpath spanningtree; it is no more, and sometimes significantly less, than the cost of constructing the shortestpath tree.
Distributed Computation for Swapping a Failing
"... Abstract. We consider the problem of computing the best swap edges of a shortestpath 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 messag ..."
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Abstract. We consider the problem of computing the best swap edges of a shortestpath 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 rerouted using the computed swap edge. There exist highly efficient serial solutions for the problem, but unfortunately because of the structures they use, there is no known (nor foreseeable) efficient distributed implementation for them. A distributed protocol exists only for finding swap edges, not necessarily optimal ones. In [6], distributed solutions to compute the swap edge that minimizes the distance from u to r have been presented. In contrast, in this paper we focus on selecting, efficiently and distributively, the best swap edge according to an objective function suggested in [13]: we choose the swap edge that minimizes the distance from u to v.
Computing All the Best Swap Edges
"... In systems using shortestpath routing tables, a single link failure is enough to interrupt the message transmission by disconnecting one or more shortestpath spanning trees. The online recomputation of an alternative path or of the entire new shortest path trees, rebuilding the routing tables acco ..."
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In systems using shortestpath routing tables, a single link failure is enough to interrupt the message transmission by disconnecting one or more shortestpath spanning trees. The online recomputation of an alternative path or of the entire new shortest path trees, rebuilding the routing tables accordingly, is rather