The Centre for Discrete Mathematics and its Applications (DIMAP)

Lead Research Organisation: University of Warwick
Department Name: Computer Science

Abstract

Discrete Mathematics plays an essential role in modelling the natural world (e.g., the genome) and the technological world (e.g., the internet), and in designing efficient solutions such as gene-sequencing algorithms and internet routing protocols. It is well known that the UK has a serious lack of capacity in this increasingly important area. This has been highlighted in three International Reviews (Computer Science, Mathematics and OR) and by independent industry reports such as that from the Smith Institute. Discrete Mathematics is a fundamentally multi-disciplinary activity. The close connections among algorithmic work being done primarily in computer science departments, combinatorial work primarily in mathematics departments, and optimisation work primarily in OR research groups in business schools, strongly suggest that the lack of capacity in these inter-related areas will be best addressed by developing a new centre with a unified, collaborative strategy. The EPSRC Science and Innovation scheme, focussing on both the interface of mathematics and computer science, and the fundamentals of operational research, reinforces this view. We propose to enhance capacity in this area substantially by founding the Centre for Discrete Mathematics and its Applications, rooted in three internationally recognised departments at the University of Warwick: Computer Science, Mathematics and the Business School. The key deliverables resulting from an initial investment of 3.62M from EPSRC/HEFCE, combined with substantial and continuing support by the University, will be:o a strong multi-disciplinary research centre in the adjacent new Computer Science and Mathematics buildings, directed by an Executive Team of Profs M Paterson FRS, AM Stuart, B Chen and Dr LA Goldberg supporting an internationally competitive programme of research in discrete modelling, algorithmic analysis and operational research;o the recruitment of three new lecturers, one in each department, on attractive terms and with permanent contracts to ensure highest quality appointments; o the recruitment of a new professor in Discrete Mathematics and its Applications in Algorithms within the Department of Computer Science;o an ongoing stream of postdoctoral RA's, building from an initial group of four to be recruited under the EPSRC/HEFCE grant;o a training strategy comprising: - a doctoral training centre offering 4-year PhD's. Two new students would be recruited each year for 5 years under the EPSRC/HEFCE grant, with others funded through CASE awards and the DTA programme; - a new stream within the 4-year Computer Science MEng degree with modules from mathematics and OR and focussing on discrete mathematics;o an Industrial Affiliates Programme, for industrial and other users to communicate their needs within the discrete mathematics area, and to collaborate with the Centre in developing solutions and transferring knowledge;o the development of collaborations, rooted in discrete maths, involving researchers at other UK universities.Strong management by the Executive Team will ensure that the Centre delivers impact through high quality research advancing knowledge in discrete mathematics, algorithms, and fundamentals of operational research and giving a significant boost to UK industry, capacity by increasing the UK's production of trained researchers in this area, sustainability by securing the long-term future through research and training, knowledge transfer via the usual publication routes and the Industrial Affiliates Programme, and timeliness by ensuring that projected schedules are met to address the UK's current problems. The added value from this Award would arise from the opportunity to focus and coordinate the excellent research currently undertaken across three departments.

Publications

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Chlamtác E (2018) The Densest $k$-Subhypergraph Problem in SIAM Journal on Discrete Mathematics

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Christofides D (2014) Hamilton cycles in dense vertex-transitive graphs in Journal of Combinatorial Theory, Series B

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CZUMAJ A (2012) APPROXIMATION ALGORITHMS FOR BUY-AT-BULK GEOMETRIC NETWORK DESIGN in International Journal of Foundations of Computer Science

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CZUMAJ A (2010) Testing Expansion in Bounded-Degree Graphs in Combinatorics, Probability and Computing

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Czumaj A (2016) Encyclopedia of Algorithms

 
Description DIMAP - which is the research centre funded by this EPSRC project - is a very successful research centre that enhanced Warwick's and UK's reputation in mathematical and computer science communities in the UK, in Europe, and around the world. It promotes cutting edge research in discrete mathematics and combinatorics, theoretical aspects of computer science, and mathematical aspects of operations research. Its positive impact on the UK mathematics scene has been cited in the International Reviews of Mathematical Sciences 2010 and DIMAP is widely recognized as a UK centre of excellence in algorithms.

Since its creation in 2007, DIMAP has become a recognised brand name in the mathematical and computer science communities around the world. Its excellent research environment - thanks to its renowned academic staff and its scientific activities - made DIMAP an excellent place to work at and visit. Largely thanks to DIMAP, Warwick has succeeded in several high profile appointments, like Dr Coja-Oghlan (ERC winner), Prof Cormode (ERC winner), Dr Georgakopoulos (ERC winner), Prof Král (ERC winner)', Prof Pikhurko (ERC winner), Dr Räcke, Prof Sviridenko, doubling the number of Warwick academic staff in core DIMAP areas. Most of DIMAP key members have significant individual research grants (which is not necessarily a UK standard in theoretical areas as those in the focus of DIMAP), including several ERC grants, many EPSRC grants, Royal Society Wolfson Merit Awards, etc. Grant income of DIMAP members together with the excellent research environment in DIMAP and its reputation, allowed DIMAP to maintain a steady number of high quality postdocs and PhD students. It's extremely unlikely that these things could have happened without DIMAP.

DIMAP's research activities, like its extensive programme of scientific seminars and international workshops and conferences, have brought to the UK and to Warwick many leading researchers from around the world, including Turing Award winners, Nevanlinna Prize winners, Gödel Prize winners, European Prize in Combinatorics winners, etc.

DIMAP has also played key role in establishing in October 2008 a new BSc degree course Discrete Mathematics, offered jointly by the Department of Computer Science and the Warwick Mathematics Institute. Current total number of students is over 100 across all years.
Exploitation Route The funding allowed the UK to enhance its international standing in discrete mathematics, theoretical computer science, and mathematical aspects of OR. We believe that this will have a positive long-term impact on the UK research in these areas and beyond, and will allow the UK to be one of the most world best centres of excellence in the very hot areas on the interface of mathematics, computer science, and operational research.
Sectors Digital/Communication/Information Technologies (including Software),Other

URL http://www2.warwick.ac.uk/dimap/