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In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.
In this graph, the widest path from Maldon to Feering has bandwidth 29, and passes through Clacton, Tiptree, Harwich, and Blaxhall. In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight of the minimum-weight edge in the path.
When using a path length that is shorter than 10mm, the resultant OD will be reduced by a factor of 10/path length. Using the example above with a 3 mm path length, the OD for the 100 μg/mL sample would be reduced to 0.6. To normalize the concentration to a 10mm equivalent, the following is done: 0.6 OD X (10/3) * 50 μg/mL=100 μg/mL
If x = 55 units then CSPF will give path A → D → E → C. If x = 90 units then CSPF will give path A → D → E → F → C. In all of these cases OSPF and IS-IS will result in path A → B → C. However, if the link costs in this topology are different, CSPF may accordingly determine a different path.
All these models had one thing in common: they all predicted very short average path length. [1] The average path length depends on the system size but does not change drastically with it. Small world network theory predicts that the average path length changes proportionally to log n, where n is the number of nodes in the network.
Given a directed graph G = (V, E), a path cover is a set of directed paths such that every vertex v ∈ V belongs to at least one path. Note that a path cover may include paths of length 0 (a single vertex). [1] A path cover may also refer to a vertex-disjoint path cover, i.e., a set of paths such that every vertex v ∈ V belongs to exactly ...
The path length of a simple conditional instruction would normally be considered as equal to 2, [citation needed] one instruction to perform the comparison and another to take a branch if the particular condition is satisfied. The length of time to execute each instruction is not normally considered in determining path length and so path length ...
Conversely, if H has an induced path or cycle of length k, any maximal set of nonadjacent vertices in G from this path or cycle forms an independent set in G of size at least k/3. Thus, the size of the maximum independent set in G is within a constant factor of the size of the longest induced path and the longest induced cycle in H.