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K.B. Lakshmanan, K. Thulasiraman, M.A. Comeau, "An Efficient Distributed Protocol for Finding Shortest Paths in Networks with Negative Weights," IEEE Transactions on Software Engineering, vol. 15, no. 5, pp. 639644, May, 1989.  
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@article{ 10.1109/32.24713, author = {K.B. Lakshmanan and K. Thulasiraman and M.A. Comeau}, title = {An Efficient Distributed Protocol for Finding Shortest Paths in Networks with Negative Weights}, journal ={IEEE Transactions on Software Engineering}, volume = {15}, number = {5}, issn = {00985589}, year = {1989}, pages = {639644}, doi = {http://doi.ieeecomputersociety.org/10.1109/32.24713}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Software Engineering TI  An Efficient Distributed Protocol for Finding Shortest Paths in Networks with Negative Weights IS  5 SN  00985589 SP639 EP644 EPD  639644 A1  K.B. Lakshmanan, A1  K. Thulasiraman, A1  M.A. Comeau, PY  1989 KW  efficient distributed protocol; negative weights; distributed algorithms; singlesource shortestpath problem; asynchronous directed network; edges; cycle; worst case; unbounded message complexity; synchronous version; ChandyMisra algorithm; nodes; time complexities; efficient synchronizer; asynchronous protocol; computational complexity; directed graphs; distributed processing; protocols VL  15 JA  IEEE Transactions on Software Engineering ER   
The design is discussed of distributed algorithms for the singlesource shortestpath problem to run on an asynchronous directed network in which some of the edges may be associated with negative weights, and thus in which a cycle of negative total weight may also exist. The only existing solution in the literature for this problem is due to K.M. Chandy and J. Misra (1982), and it has, in the worst case, an unbounded message complexity. A synchronous version of the ChandyMisra algorithm is described and studied, and it is proved that for a network with m edges and n nodes, the worst case message and time complexities of this algorithm are O(mn) and O(n), respectively. This algorithm is then combined with an efficient synchronizer to yield an asynchronous protocol that retains the same message and time complexities.
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