Questions tagged [simplex]

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43
votes
6answers
20k views

Complexity of the simplex algorithm

What is the upper bound on the simplex algorithm for finding a solution to a Linear Program? How would I go about finding a proof for such a case? It seems as though the worst case is if each vertex ...
31
votes
3answers
2k views

Consequences of existence of a strongly polynomial algorithm for linear programming?

One of the holy grails of algorithm design is finding a strongly polynomial algorithm for linear programming, i.e., an algorithm whose runtime is bounded by a polynomial in the number of variables and ...
18
votes
1answer
516 views

The structure of pathological instances for simplex algorithms

As far as I understand, all know deterministic pivot rules for simplex algorithms have specific inputs on which the algorithm requires exponential time (or at least not polynomial) to find the optimum....
14
votes
2answers
2k views

Justification for the Hungarian method (Kuhn-Munkres)

I wrote an implementation of the Kuhn-Munkres algorithm for the minimum-weight bipartite perfect matching problem based on lecture notes I found here and there on the web. It works really well, even ...