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In mathematics, the Cheeger constant (also Cheeger number or isoperimetric number) of a graph is a numerical measure of whether or not a graph has a "bottleneck". The Cheeger constant as a measure of "bottleneckedness" is of great interest in many areas: for example, constructing well-connected networks of computers, card shuffling.
A bottleneck edge is the highest weighted edge in a spanning tree. A spanning tree is a minimum bottleneck spanning tree if the graph does not contain a spanning tree with a smaller bottleneck edge weight. [1] For a directed graph, a similar problem is known as Minimum Bottleneck Spanning Arborescence (MBSA).
The Shifting Bottleneck Heuristic is a procedure intended to minimize the time it takes to do work, or specifically, the makespan in a job shop.The makespan is defined as the amount of time, from start to finish, to complete a set of multi-machine jobs where machine order is pre-set for each job.
The bottleneck is the minimum residual capacity of all the edges in a given augmenting path. [2] See example explained in the "Example" section of this article. The flow network is at maximum flow if and only if it has a bottleneck with a value equal to zero. If any augmenting path exists, its bottleneck weight will be greater than 0.
If, in addition, each number in the sequence exceeds the sum of all smaller numbers, then the bottleneck solution will also equal the usual TSP solution. For instance, such a result may be attained by resetting each weight to n i where n is the number of vertices in the graph and i is the rank of the original weight of the edge in the sorted ...
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.
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The information bottleneck method is a technique in information theory introduced by Naftali Tishby, Fernando C. Pereira, and William Bialek. [1] It is designed for finding the best tradeoff between accuracy and complexity (compression) when summarizing (e.g. clustering) a random variable X, given a joint probability distribution p(X,Y) between X and an observed relevant variable Y - and self ...