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The critical path method (CPM), or critical path analysis (CPA), is an algorithm for scheduling a set of project activities. [1] A critical path is determined by identifying the longest stretch of dependent activities and measuring the time [ 2 ] required to complete them from start to finish.
Therefore, the longest path problem is NP-hard. The question "does there exist a simple path in a given graph with at least k edges" is NP-complete. [2] In weighted complete graphs with non-negative edge weights, the weighted longest path problem is the same as the Travelling salesman path problem, because the longest path always includes all ...
Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
Total float is associated with the path. [ 2 ] : 508 [ 1 ] : 183 If a project network chart/diagram has 4 non-critical paths, then that project would have 4 total float values. The total float of a path is the combined free float values of all activities in a path.
Critical path drag is a project management metric [1] developed by Stephen Devaux as part of the Total Project Control (TPC) approach to schedule analysis and compression [2] in the critical path method of scheduling. Critical path drag is the amount of time that an activity or constraint on the critical path is adding to the project duration ...
During a (e.g. Monte Carlo) simulation tasks can join or leave the critical path for any given iteration. The Criticality Index expresses how often a particular task was on the Critical Path during the analysis. Tasks with a high Criticality Index are more likely to cause delay to the project as they are more likely to be on the Critical Path.
From a dynamic programming point of view, Dijkstra's algorithm for the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method. [8] [9] [10] In fact, Dijkstra's explanation of the logic behind the algorithm, [11] namely Problem 2.
This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are thousands of such problems known, this list is in no way comprehensive. Many problems of this type can be found in Garey & Johnson (1979).