Approximating the domatic number
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The Maximum Edge-Disjoint Paths Problem in Bidirected Trees
SIAM Journal on Discrete Mathematics
On 2-Coverings and 2-Packings of Laminar Families
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Restricted strip covering and the sensor cover problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Polychromatic colorings of plane graphs
Proceedings of the twenty-fourth annual symposium on Computational geometry
Max-Weight Integral Multicommodity Flow in Spiders and High-Capacity Trees
Approximation and Online Algorithms
A constructive proof of the Lovász local lemma
Proceedings of the forty-first annual ACM symposium on Theory of computing
Disjoint bases in a polymatroid
Random Structures & Algorithms
Decomposing Coverings and the Planar Sensor Cover Problem
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Tight lower bounds for the size of epsilon-nets
Proceedings of the twenty-seventh annual symposium on Computational geometry
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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A colouring of a hypergraph's vertices is polychromatic if every hyperedge contains at least one vertex of each colour; the polychromatic number is the maximum number of colours in such a colouring. Its dual, the cover-decomposition number, is the maximum number of disjoint hyperedge-covers. In geometric settings, there is extensive work on lower-bounding these numbers in terms of their trivial upper bounds (minimum hyperedge size & degree). Our goal is to get good lower bounds in natural hypergraph families not arising from geometry. We obtain algorithms yielding near-tight bounds for three hypergraph families: those with bounded hyperedge size, those representing paths in trees, and those with bounded VC-dimension. To do this, we link cover-decomposition to iterated relaxation of linear programs via discrepancy theory.