Jakub Marecek

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We present improved algorithms based on the primal-dual paradigm, where the Handbook of Approximation Algorithms and Metaheuristics, Chapman. H.-J. Böckenhauer, J. Hromkovič, S. Seibert: Stability of approximation. In: T. F. Gonzalez (ed.): Handbook of Approximation Algorithms and Metaheuristics. Handbook of Approximation Algorithms and MetaHeuristics.(More)
Formulating the alternating current optimal power flow (ACOPF) as a polynomial optimization problem makes it possible to solve large instances in practice and to guarantee asymptotic convergence in theory. We formulate the ACOPF as a degree-two polynomial program and study two approaches to solving it via convexifications. In the first approach, we tighten(More)
This paper describes a branch-and-cut procedure for an extension of the bounded colouring problem, generally known as curriculum-based university course timetabling. In particular, we focus on Udine Course Timetabling [di Gaspero and Schaerf, J. Math. Model. Algorithms 5:1], which has been used in Track 3 of the 2007 International Timetabling Competition.(More)
In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a(More)
For many problems in Scheduling and Timetabling the choice of a mathematical programming formulation is determined by the formulation of the graph colouring component. This paper briefly surveys seven known integer programming formulations of vertex colouring and introduces a new formulation using “supernodes”. In the definition of George and McIntyre [SIAM(More)
In this work we propose a distributed randomized block coordinate descent method for minimizing a convex function with a huge number of variables/coordinates. We analyze its complexity under the assumption that the smooth part of the objective function is partially block separable, and show that the degree of separability directly influences the complexity.(More)
Many complex timetabling problems, such as university course timetabling [1, 2] and employee rostering [3], have an underpinning bounded graph colouring component, a pattern penalisation component and a number of side constraints. The bounded graph colouring component corresponds to hard constraints such as “each student attends all events of courses of his(More)
Vertex colouring is a well-known problem in combinatorial optimisation, whose alternative integer programming formulations have recently attracted considerable attention. This paper briefly surveys seven known formulations of vertex colouring and introduces a new formulation of vertex colouring using a suitable clique partition of the graph. This(More)