ISCO 2012: Combinatorial Optimization pp 189-200

# Fast Separation Algorithms for Three-Index Assignment Problems

• Trivikram Dokka
• Ioannis Mourtos
• Frits C. R. Spieksma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)

## Abstract

In polyhedral combinatorics, the polytope related to a combinatorial optimization problem is examined in order to obtain families of valid inequalities. To incorporate such families of inequalities within a ‘Branch & Cut’ algorithm requires one further step: that of deriving an algorithm which determines whether an inequality of a specific family is violated by a given vector (the separation problem). The idea put forward in this work is to consider a compact representation of the given vector, and measure the complexity of a separation algorithm in terms of this compact representation. We illustrate the idea on the separation of known inequalities for the three index assignment polytope. It turns out that we find new separation algorithms with better complexities than the current ones (that were called best possible).

## Keywords

Assignment Problem Valid Inequality Separation Problem Separation Algorithm Single Machine Schedule Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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