Topics in Algorithms, Complexity, and Combinatorial Optimisation
Prof Zivny is willing to supervise in the area of algorithms, complexity, and combinatorial optimisation. In particular, on problems related to convex relaxations (linear and semidefinite programming relaxations), submodular functions, and algorithms for and complexity of homomorphisms problems and Constraint Satisfaction Problems. Examples of supervised projects involve extensions of min-cuts in graphs, analysis of randomised algorithms for graph and hypergraph colourings, and sparsification of graphs and hypergraphs. The projects would suit mathematically oriented students, with interest in rigorous analysis of algorithms and applications of combinatorics and probabilistic methods to computer science.