Abstract
We study the combinatorial problem of finding an arrangement of distinct integers into the d-dimensional N-cube so that the maximal variance of the numbers on each ℓ-dimensional section is minimized. Our main tool is an inequality on the Laplacian of a Shannon product of graphs, which might be a subject of independent interest. We describe applications of the inequality to multiple description scalar quantizers (MDSQ), to get bounds on the bandwidth of products of graphs, and to balance edge-colorings of regular, d-uniform, d-partite hypergraphs.
Original language | English (US) |
---|---|
Pages (from-to) | 110-118 |
Number of pages | 9 |
Journal | Discrete Applied Mathematics |
Volume | 156 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 2008 |
Keywords
- Graph product
- Labeling
- Variance
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics