Locality in distributed graph algorithms
SIAM Journal on Computing
SIAM Journal on Computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
End-to-end packet-scheduling in wireless ad-hoc networks
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Characterizing achievable rates in multi-hop wireless mesh networks with orthogonal channels
IEEE/ACM Transactions on Networking (TON)
Half-space proximal: a new local test for extracting a bounded dilation spanner of a unit disk graph
OPODIS'05 Proceedings of the 9th international conference on Principles of Distributed Systems
Local construction of planar spanners in unit disk graphs with irregular transmission ranges
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Localized Delaunay triangulation with application in ad hoc wireless networks
IEEE Transactions on Parallel and Distributed Systems
Local algorithms for edge colorings in UDGs
Theoretical Computer Science
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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. 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.