You want a set of lines that connects all your offices with a minimum total cost.
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of the 33rd International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM'07), Lecture Notes in Computer Science, Band 4362 , S.
We consider the problem of updating a directed minimum cost spanning tree (DMST), when edges are deleted from or inserted to a weighted directed graph.
This problem apart from being a classic for directed graphs, is to the best of our knowledge a wide open aspect for the field of dynamic graph algorithms.
The book tries to keep things simpler, so it only describes one algorithm but (in my opinion) doesn't do a very good job of it.
I'll go through three simple classical algorithms (spending not so much time on each one).
The standard application is to a problem like phone network design.
You have a business with several offices; you want to lease phone lines to connect them up with each other; and the phone company charges different amounts of money to connect different pairs of cities.
Our contributions include results on the hardness of updates, a dynamic algorithm for updating a DMST, and detailed experimental analysis of the proposed algorithm exhibiting a speedup factor of at least 2 in comparison with the static practice.
o---o o---o o o o---o | | | | | | | | | | | | | | | | | | o o o---o o---o o---o o---o o o o o o o \ / |\ / \ / \ /| X | X X X | / \ |/ \ / \ / \| o o o o o---o o o o o o---o o o o---o |\ | / | /| \ | \ | / | / | \ | \| / |/ | \ o o o---o o o o---o o---o o o o o o---o |\ | / \ | /| | \ | / \ | / | | \ |/ \| / | o o o---o o---o o o Now suppose the edges of the graph have weights or lengths.
The weight of a tree is just the sum of weights of its edges. The problem: how to find the minimum length spanning tree?
This problem can be solved by many different algorithms. There are several "best" algorithms, depending on the assumptions you make: These algorithms are all quite complicated, and probably not that great in practice unless you're looking at really huge graphs.