Local edge colouring of Yao-like subgraphs of Unit Disk Graphs

J. Czyzowicz, S. Dobrev, E. Kranakis, J. Opatrny, J. Urrutia
2009 Theoretical Computer Science  
The focus of the present paper is on providing a local deterministic algorithm for colouring the edges of Yao-like subgraphs of Unit Disc Graphs. These are geometric graphs such that for some positive integers l, k the following property holds at each node v: if we partition the unit circle centered at v into 2k equally sized wedges then each wedge can contain at most l points different from v. We assume that the nodes are location aware, i.e. they know their Cartesian coordinates in the plane.
more » ... The algorithm presented is local in the sense that each node can receive information emanating only from nodes which are at most a constant (depending on k and l, but not on the size of the graph) number of hops away from it, and hence the algorithm terminates in a constant number of steps. The number of colours used is 2kl + 1 and this is optimal for local algorithms (since the maximal degree is 2kl and a colouring with 2kl colours can only be constructed by a global algorithm), thus showing that in this class of graphs the price for locality is only one additional colour.
doi:10.1016/j.tcs.2008.11.008 fatcat:v2u4d6fq7fhkdpodooib34mh2e