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A New Algorithm for Solving Critical Path

2013-09-19
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By defining the concept of node coding graph, a new algorithm for solving critical paths that does not require topological sorting is proposed. The algorithm expands the storage structure of the adjacency list of the graph so that the storage of the graph and the algorithm solving process share the same storage space. Starting from the source node of the graph, all nodes in the graph are encoded recursively using the weighted maximum operation rule and breadth-first recursion. After the coding graph is generated, reverse search is used to find all critical paths and lengths from the source point to the sink point. This algorithm is simpler and more intuitive than existing algorithms, requires less storage space, and the algorithm time complexity is reduced to O(n+e), which is better than the existing algorithm\'s O(n2). Keywords: coding graph; critical path; AOE network; breadth-first search; time complexity

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