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<p><b>Abstract</b>—Knot detection in a distributed graph is an important problem and finds applications in deadlock detection in several areas such as store-and-forward networks, distributed simulation, and distributed database systems. This paper presents an efficient distributed algorithm to detect if a node is part of a knot in a distributed graph. The algorithm requires 2e messages and a delay of 2(d+1) message hops to detect if a node in a distributed graph is in a knot (here, e is the number of edges in the reachable part of the distributed graph and <tmath>d</tmath> is its diameter). A significant advantage of this algorithm is that it not only detects if a node is involved in a knot, but also finds exactly which nodes are involved in the knot. Moreover, if the node is not involved in a knot, but is only involved in a cycle, then it finds the nodes that are in a cycle with that node. We illustrate the working of the algorithm with examples. The paper ends with a discussion on how the information about the nodes involved in the knot can be used for deadlock resolution and also on the performance of the algorithm.</p>
Distributed graph, distributed systems, knot detection, deadlock detection, distributed algorithms, distributed simulation.

M. Singhal and D. Manivannan, "An Efficient Distributed Algorithm for Detection of Knots and Cycles in a Distributed Graph," in IEEE Transactions on Parallel & Distributed Systems, vol. 14, no. , pp. 961-972, 2003.
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