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- Title
Graphical designs and gale duality.
- Authors
Babecki, Catherine; Thomas, Rekha R.
- Abstract
A graphical design is a subset of graph vertices such that the weighted averages of certain graph eigenvectors over the design agree with their global averages. We use Gale duality to show that positively weighted graphical designs in regular graphs are in bijection with the faces of a generalized eigenpolytope of the graph. This connection can be used to organize, compute and optimize designs. We illustrate the power of this tool on three families of Cayley graphs – cocktail party graphs, cycles, and graphs of hypercubes – by computing or bounding the smallest designs that average all but the last eigenspace in frequency order.
- Subjects
WINDSTORMS; REGULAR graphs; CAYLEY graphs; HYPERCUBES; COCKTAIL parties; POWER tools; HAMMING codes
- Publication
Mathematical Programming, 2023, Vol 200, Issue 2, p703
- ISSN
0025-5610
- Publication type
Article
- DOI
10.1007/s10107-022-01861-0