Abstract
We provide a framework for online conflict-free colouring of any hypergraph. We introduce the notion of a degenerate hypergraph, which characterizes hypergraphs that arise in geometry. We use our framework to obtain an efficient randomized online algorithm for conflict-free colouring of any k-degenerate hypergraph with n vertices. Our algorithm uses O(k log n) colours with high probability and this bound is asymptotically optimal. Moreover, our algorithm uses O(k log k log n) random bits with high probability. We introduce algorithms that are allowed to perform a few recolourings of already coloured points. We provide deterministic online conflict-free colouring algorithms for points on the line with respect to intervals and for points on the plane with respect to half-planes (or unit disks) that use O(log n) colours and perform a total of at most O(n) recolourings.
Original language | English |
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Pages (from-to) | 493-516 |
Number of pages | 24 |
Journal | Combinatorics Probability and Computing |
Volume | 19 |
Issue number | 4 |
DOIs | |
State | Published - 1 Jul 2010 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics