Minimum Spanning Tree Search Task
A Minimum Spanning Tree Search Task is a graph search optimization task that requires finding a minimum spanning tree within a connected undirected graph.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Minimum_spanning_tree Retrieved:2015-12-13.
- A minimum spanning tree is a spanning tree of a connected, undirected graph. It connects all the vertices together with the minimal total weighting for its edges.
A single graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree. A minimum spanning tree (MST) or minimum weight spanning tree is then a spanning tree with weight less than or equal to the weight of every other spanning tree. More generally, any undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of minimum spanning trees for its connected components.
There are quite a few use case of minimum spanning tree, one example would be a telecommunications company which is trying to lay out cables in new neighborhood. If it is constrained to bury the cable only along certain paths (e.g. along roads), then there would be a graph representing which points are connected by those paths. Some of those paths might be more expensive, because they are longer, or require the cable to be buried deeper; these paths would be represented by edges with larger weights. Currency is an acceptable unit for edge weight — there is no requirement for edge lengths to obey normal rules of geometry such as the triangle inequality. A spanning tree for that graph would be a subset of those paths that has no cycles but still connects to every house; there might be several spanning trees possible. A minimum spanning tree would be one with the lowest total cost, thus would represent the least expensive path for laying the cable.
- A minimum spanning tree is a spanning tree of a connected, undirected graph. It connects all the vertices together with the minimal total weighting for its edges.