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Optimizing hypergraph-based polynomials modeling job-occupancy in queuing with redundancy scheduling

Brosch,Daniel
; 
Laurent,Monique
; 
Steenkamp,Andries
Abstract
We investigate two classes of multivariate polynomials with variables indexed by the edges of a uniform hypergraph and coefficients depending on certain patterns of unions of edges. These polynomials arise naturally to model job-occupancy in some queuing problems with redundancy scheduling policies. The question, posed by Cardinaels, Borst, and van Leeuwaarden in [Redundancy Scheduling with Locally Stable Compatibility Graphs, arXiv preprint, 2020], is to decide whether their global minimum over the standard simplex is attained at the uniform probability distribution. By exploiting symmetry properties of these polynomials we can give a positive answer for the first class and partial results for the second one, where we in fact show a stronger convexity property of these polynomials over the simplex.
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2021-09-07
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Tilburg University Research Output Collection
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Keywords
Convex polynomial, Polynomial optimization, Symmetry, Terwilliger algebra
Citation
Brosch, D, Laurent, M & Steenkamp, A 2021, 'Optimizing hypergraph-based polynomials modeling job-occupancy in queuing with redundancy scheduling', SIAM Journal on Optimization, vol. 31, no. 3, pp. 2227-2254. https://doi.org/10.1137/20M1369592
URI
https://hdl.handle.net/20.500.14602/75330
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