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Simplicial Pivoting Algorithms for Integer Programming

Article Outline

Keywords

Triangulations
Labelings
Integer Labeling
Vector Labeling
Pivoting
Noncycling Arguments
Max-Closed Sets
Unimodular Max-Closed Form Transformations
See also
References

Keywords Simplicial algorithms - Integer programming - Knapsack problem - Horn formulas

Simplicial path following methods are relatively new in the area of integer programming (cf. Integer programming). They are based on a triangulation of Euclidean space and a pivoting algorithm which, for a restrictive class of problems, terminates with an integral solution or shows that no such solution exists. The path constructed consists of a sequence of neighboring simplices , the vertices of which are integral lattice points.

Simplicial methods originated in fixed point theory , where they are used to approximate fixed points of continuous mappings [7,18].

In the area of continuous mathematics they have been applied successfully