Algorithms and Theory

The Foundations and Algorithms group investigates mathematical underpinnings of computing, with the goal of designing algorithms and computational approaches to problems of engineering, social and natural sciences, medicine and healthcare. The overarching goal of the group is to build a mathematically sound foundation for the design of modern computing systems, and to develop analytic frameworks for their correctness, performance, reliability and security. Current research topics include design of efficient data structures and algorithms, characterizing the complexity of computational problems, exploring the fundamental limits of quantum computers, and design of secure and scalable cryptographic protocols.

Affilated Labs: 
Center for Geometric Computing


Wim van Dam's research focuses on the theory of quantum computation and quantum communication. His main interest is in the development of new quantum algorithms that give an exponential speed-up when compared with traditional, classical algorithms.

Bijective and enumerative combinatorics, algorithms, computational geometry. 

Prof. Gilbert’s principal research contributions have been in algorithms and software for combinatorial and numerical problems. He has done fundamental work in sparse matrix techniques; he was a primary architect and developer of Matlab’s sparse matrix capability and of the SuperLU solver library

The main research contributions of Professor Gonzalez include the development of exact and approximation algorithms, and establishing complexity results for a wide range of problems arising in several different application areas.

Dr. Daniel Lokshtanov's research is in Theoretical Computer Science and Discrete Mathematics, most of it in Algorithmic Graph Theory and Parameterized Complexity.

The use of geometry and graph theory, as conceptual tools and an algorithmic lens, has proved invaluable in a number of scientific and engineering disciplines.