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SEMIRING FRAMEWORKS AND ALGORITHMS FOR SHORTESTDISTANCE PROBLEMS
, 2002
"... We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorit ..."
Abstract

Cited by 76 (20 self)
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We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the kshortest distances in a directed graph. It can be used to solve singlesource shortestdistance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.
RREACT: A Distributed Protocol for Rapid Restoration of Active Communication Trunks
, 1993
"... Commercial telecommunications networks have tight realtime requirements for restoration after a failure. The problem of finding the available restoration paths and reassigning the interrupted traffic within such tight realtime requirements places difficult demands on the restoration protocol emplo ..."
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Cited by 4 (2 self)
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Commercial telecommunications networks have tight realtime requirements for restoration after a failure. The problem of finding the available restoration paths and reassigning the interrupted traffic within such tight realtime requirements places difficult demands on the restoration protocol employed. This paper reviews several distributed network restoration protocols and presents a new distributed protocol called RREACT, for performing this function with a distributed algorithm which uses no prior network status or topography knowledge and which supports multiple simultaneous link restorations. Simulation results show that this protocol significantly outperforms other existing algorithms based on the SenderChooser approach, usually completing the total restoration in well under one second. In addition, enhancements to the basic algorithm are described which help to ensure nearoptimal use of network spare channel resources and address such restoration situations where a complete r...