degeneracy - • Maintaining a strongly feasible spanning...

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If there is more than one candidate for the leaving arc, then for each candidate arc ij , x’ ij = 0 . Only one of the candidate arcs leaves the tree, so the new solution has x’ ij =0 for at least one of its tree arcs. Such a solution is called a degenerate solution. They could lead to pivots with t = x f = 0 , that is no decrease in the cost. Degeneracy is necessary but not sufficient for cycling.
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Unformatted text preview: • Maintaining a strongly feasible spanning tree guarantees finite • termination and speeds up the running time • • A pivot iteration is non-degenerate if ± > 0 and is degenerate if ± = 0 • • A degenerate iteration occurs only if T is a degenerate spanning tree. • • If two arcs tie while determining the value of ± , the next spanning tree • will be degenerate....
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This note was uploaded on 01/26/2011 for the course IEOR 4004 taught by Professor Sethuraman during the Fall '10 term at Columbia.

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