We are looking for a talented and motivated student with a strong interest in the theory and practice of Integer Programming (IP). The research will be supported by the ERC grant "Towards a Quantitative Theory of Integer Programming". The goals of this research are (1) to develop a quantitative theory that can explain the effectiveness of the prevalent techniques used for solving IPs (e.g. branch & bound, cutting planes, diving heuristics, etc.), (2) to develop new and effective techniques for solving IPs and (3) to build new connections between the study of IP, theoretical computer science and optimization.

The research projects are designed to be interdisciplinary and are expected to require combining techniques from various areas of optimization (first order methods, interior point methods, simplex algorithms), theoretical computer science (discrepancy theory, fixed parameter tractability, smoothed analysis) and geometry (convex geometry, geometry of Euclidean lattices). Some sample research questions include:

• Can one obtain non-trivial upper bounds on the size of branch & bound trees produced by standard branching rules?
• Is there a cutting plane based polynomial time approximation scheme for the metric traveling salesman problem? More generally, can one develop a cutting plane framework with provable convergence guarantees?
• Can one automate basic FPT algorithms using the branch & bound framework?
• Can one demonstrate the efficiency of the simplex method for solving related sequences of linear programs (as one would encounter within branch & bound or cutting plane generation)?
• Can one develop practical rounding heuristics using discrepancy minimization algorithms?
• Is there a 2O(n) -time algorithm for general integer programming?

Supervised by: Daniel Dadush (website)

The PhD candidate is required to have a strong background in at least one of the following areas: optimization, theoretical computer science or discrete mathematics. Research experience within the domain of IP (theory or practice) is a plus. The most important qualification however is an open mind and the ability to pick up new material quickly. Candidates are expected to have an excellent command of English, and good academic writing and presentation skills. The PhD candidate will be expected to conduct research on topics relevant to the above agenda, to publish this research at either top conferences or journals, and defend a PhD thesis within 4 years.

Fixed-term contract: 4 years.

The terms of employment are in accordance with the Dutch Collective Labour Agreement for Research Centres ("CAO-onderzoeksinstellingen"). The initial labour agreement will be for a period of 18 months. After a positive evaluation, the agreement will extended by 30 months. The gross monthly salary, for a PhD student on a full time basis, is €2,291 during the first year and increases to €2,937 over the four year period.

Employees are also entitled to a holiday allowance of 8% of the gross annual salary and a year-end bonus of 8.33%. CWI offers attractive working conditions, including flexible scheduling and help with housing for expat employees.

Please visit our website for more information about our terms of employment: https://www.cwi.nl/jobs/terms-of-employment

Centrum Wiskunde & Informatica (CWI) is the Dutch national research institute for mathematics and computer science and is part of the Institutes Organisation of NWO. The mission of CWI is to conduct pioneering research in mathematics and computer science, generating new knowledge in these fields and conveying it to trade, industry, and society at large.

CWI is an internationally oriented institute, with 160 scientists from approximately 27 countries. The facilities are first-rate and include excellent IT support, career planning, training, and courses.

CWI is located at Science Park Amsterdam that is presently developing into a major location of research in the natural sciences in The Netherlands, housing the sciences of the University of Amsterdam and of the Vrije Universiteit as well as several other national research institutes next to CWI.

For more information about the N&O research group at CWI, please visit our website.