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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 Bottleneck traveling salesman problem (bottleneck TSP) is a problem in discrete or combinatorial optimization. The problem is to find the Hamiltonian cycle (visiting each node exactly once) in a weighted graph which minimizes the weight of the highest-weight edge of the cycle. [ 1 ]
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.
The decision version of the TSP (where given a length L, the task is to decide whether the graph has a tour whose length is at most L) belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (but no more than exponentially) with the number of ...
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.
A planar graph and its minimum spanning tree. Each edge is labeled with its weight, which here is roughly proportional to its length. A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. [1]
Each node on the graph represents a task that is part of the job, the second number confirms the job being performed and the first number indicates what machine is being used for this task. At this point, the initial throughput time of each job should be calculated by adding up the processing times that the job takes on each of the machines (or ...
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.