Professor Colin McDiarmid
Discrete mathematics, random structures, algorithms and complexity, combinatorial optimisation, mathematics of operational research.
1. 'Random channel assignment problems' - In one model for random radio channel assignment, points corresponding to transmitters are thrown down at random in the plane, and we are to assign a radio channel to each point so that neighbouring points get different channels (to avoid interference).
'Random channel assignment in the plane', Random Structures and Algorithms 22 (2003) 187 – 212.
In the second model, each pair of transmitters u and v are given minimum distance 0,1 or 2 at random, and we are assign channels 1, 2, 3, .. so that the channels assigned to u and v must differ by at least the specified minimum distance (again, to avoid interference). 'On the span of random channel assignment problem', Combinatorica, 27 (2007) 183-203.
2. Load balancing - A simple but powerful method for minimising the maximum load of a processor involves picking two processor queues at random and joining the shorter.
'On the power of two choices': balls and bins in continuous time, Annals of Applied Probability 15 (2005) 1733-1764. (Joint with Malwina Luczak.)
'On the maximum queue length in the supermarket model, Annals of Probability 34 (2006) 493-527. (Joint with Malwina Luczak.)
3. Random planar graphs - There has been a huge and successful endeavour investigating random graphs where edges appear independently, but what if , say, we wish to find typical properties of planar graphs after 'Random planar graphs'?
'Random planar graphs', J. Combinatorial Theory B 93 (2005) 187-206. (Joint with Angelika Steger and Dominic Welsh.)
'Random graphs on surfaces', J. Combinatorial Theory B, 98 (2008) 778-797.
Random graphs from a minor-closed class, Combinatorics, Probability and Computing, 19 (2010) 87-98
List of publications (recent and some not so recent)
I have been based in Oxford as a Fellow of Corpus Christi College since 1989 (having previously been a Fellow of Wolfson College), closely associated with both the Mathematical Institute and the Department of Statistics. I was Head of Department from 2005 to 2009.