Kolmogorov Group

Discrete Optimization

When we step out into the street, we automatically judge the distance and speed of cars. For computers, estimating the depth of objects in an image requires complex computations. A popular approach for tackling this problem is to use discrete optimization algorithms – the research focus of the Kolmogorov group.

The work of Vladimir Kolmogorov’s group can be divided into three topics. The first is the development of efficient algorithms for inference in graphical models and combinatorial optimization problems. Some of their techniques are widely used in computer vision and other areas, for example the “Boykov-Kolmogorov” maximum flow algorithm and the “TRW-S” algorithm for MAP inference in pairwise graphical models. Kolmogorov‘s “Blossom V” algorithm is currently the fastest technique in practice for computing a minimum cost perfect matching in a graph. Their second focus is theoretical investigations of the complexity of discrete optimization, in particular using the framework of valued constraint satisfaction problems and their variants. Finally, the Kolmogorov group has worked on applications of discrete optimization in computer vision, such as image segmentation and stereo reconstruction.

On this site:


Current Projects

Inference in graphical models | Combinatorial optimization problems | Theory of discrete optimization


Iyiola OS, Shehu Y. 2021. New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results in Mathematics. 76(2), 75. View

Izuchukwu C, Shehu Y. 2021. New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. Networks and Spatial Economics. View

Bloch-Hansen A, Samei N, Solis-Oba R. 2021. Experimental evaluation of a local search approximation algorithm for the multiway cut problem. Conference on Algorithms and Discrete Applied Mathematics. CALDAM: Conference on Algorithms and Discrete Applied MathematicsLNCS vol. 12601, 346–358. View

Shehu Y, Iyiola OS, Thong DV, Van NTC. 2020. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. View

Shehu Y, Iyiola OS. 2020. Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence. Applied Numerical Mathematics. 157, 315–337. View

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since 2014 Professor, IST Austria
2011 – 2014 Assistant Professor, IST Austria
2005 – 2011 Lecturer, University College London, UK
2003 – 2005 Assistant Researcher, Microsoft Research, Cambridge, UK
2003 PhD, Cornell University, Ithaca, U

Selected Distinctions

2018 Best paper award honorable mention at IEEE/CVF Conference on Computer Vision and Pattern Recognition
2013 ERC Consolidator Grant
2012 Koenderink Prize at the European Conference on Computer Vision for fundamental contributions to computer vision
2007 Honorable mention, outstanding student paper award (to M. Pawan Kumar) at Neural Information Processing Systems Conference
2006 – 2011 Royal Academy of Engineering/EPSRC Research Fellowship
2005 Best paper honorable mention award at IEEE Conference on Computer Vision and Pattern Recognition
2002 Best paper award at the European Conference on Computer Vision

Additional Information

Open Kolmogorov’s homepage

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