On the mean radius of permutation polytopes

Authors:
Raymond Robb
Affiliations:
Cabrini College, 610 King of Prussia Rd., Radnor, PA and Department of Mathematics, McKendree College, 701 College Rd., Lebanon, IL
Venue:
Discrete Applied Mathematics
Year:
2005

Citing 3
Cited 0

Combinatorial optimization: algorithms and complexity

Combinatorial optimization: algorithms and complexity
Approximate counting via random optimization

Random Structures & Algorithms
Integral geometry of higher-dimensional polytopes and the average case in combinatorial optimization

FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science

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Abstract

After calculating the mean value of the support function for the simplex of the coordinate vectors over the unit sphere, we find the mean for a number of polytopes, including the Birkhoff and Asymmetric Traveling Salesman polytopes, and discuss what the latter means for the corresponding Asymmetric Traveling Salesman Problem. We also discuss how to apply these results to efficiently count the vertices of certain other permutation polytopes.