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Distributed cycle detection algorithms are useful for processing large-scale graphs using a distributed graph processing system on a computer cluster (or supercomputer). Applications of cycle detection include the use of wait-for graphs to detect deadlocks in concurrent systems. [6]
In computer science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any function f that maps a finite set S to itself, and any initial value x 0 in S , the sequence of iterated function values
The Rocha–Thatte algorithm is a general algorithm for detecting cycles in a directed graph by message passing among its vertices, based on the bulk synchronous message passing abstraction. This is a vertex-centric approach in which the vertices of the graph work together for detecting cycles.
If the graph is connected, it finds a minimum spanning tree. It is a greedy algorithm that in each step adds to the forest the lowest-weight edge that will not form a cycle. [2] The key steps of the algorithm are sorting and the use of a disjoint-set data structure to detect cycles. Its running time is dominated by the time to sort all of the ...
Any vertex that is not on a directed cycle forms a strongly connected component all by itself: for example, a vertex whose in-degree or out-degree is 0, or any vertex of an acyclic graph. The basic idea of the algorithm is this: a depth-first search (DFS) begins from an arbitrary start node (and subsequent depth-first searches are conducted on ...
His contributions include the design of the Floyd–Warshall algorithm (independently of Stephen Warshall), which efficiently finds all shortest paths in a graph and his work on parsing; Floyd's cycle-finding algorithm for detecting cycles in a sequence was attributed to him as well.
If a graph contains a "negative cycle" (i.e. a cycle whose edges sum to a negative value) that is reachable from the source, then there is no cheapest path: any path that has a point on the negative cycle can be made cheaper by one more walk around the negative cycle. In such a case, the Bellman–Ford algorithm can detect and report the ...
Therefore, the special case of the zero-weight cycle problem, on graphs with no negative cycle, has a polynomial-time algorithm. [1] In contrast, for graphs that contain negative cycles, detecting a simple cycle of weight exactly 0 is an NP-complete problem. [1] This is true even when the weights are integers of polynomial magnitude.