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Distributed Computation of All Node Replacements of a Minimum Spanning Tree ⋆
"... Abstract. In many network applications the computation takes place on the minimumcost spanning tree (MST) of the network; unfortunately, a single link or node failure disconnects the tree. In this paper we consider for the first time the problem of computing all the replacement minimumcost spannin ..."
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Abstract. In many network applications the computation takes place on the minimumcost spanning tree (MST) of the network; unfortunately, a single link or node failure disconnects the tree. In this paper we consider for the first time the problem of computing all the replacement minimumcost spanning trees distributively, andwe efficiently solve the problem. We design a solution protocol and we prove that the total amount of data items communicated during the computation is O(n 2). This communication can be achieved either transmitting O(n) long messages, if the system so allows, or O(n 2) standard messages. Even in systems that do not allow long messages, the proposed protocol constitutes a significant improvement over the individual computation of the replacement trees.
Linear Time Distributed Swap Edge Algorithms ⋆
"... Abstract. In this paper, we consider the all best swap edges problem in a distributed environment. We are given a 2edge connected positively weighted network X, where all communication is routed through a rooted spanning tree T of X. If one tree edge e = {x, y} fails, the communication network will ..."
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Abstract. In this paper, we consider the all best swap edges problem in a distributed environment. We are given a 2edge connected positively weighted network X, where all communication is routed through a rooted spanning tree T of X. If one tree edge e = {x, y} fails, the communication network will be disconnected. However, since X is 2edge connected, communication can be restored by replacing e by nontree edge e ′ , called a swap edge of e, whose ends lie in different components of T − e. Of all possible swap edges of e, we would like to choose the best, as defined by the application. The all best swap edges problem is to identify the best swap edge for every tree edge, so that in case of any edge failure, the best swap edge can be activated quickly. There are solutions to this problem for a number of cases in the literature. A major concern for all these solutions is to minimize the number of messages. However, especially in faulttransient environments, time is a crucial factor. In this paper we present a novel technique that addresses this problem from a time perspective; in fact, we present a distributed solution that works in linear time with respect to the height h of T for a number of different criteria, while retaining the optimal number of messages. To the best of our knowledge, all previous solutions solve the problem in O(h 2)timein the cases we consider. 1