Carnegie Mellon University

Carnegie Mellon University offers an interdisciplinary Ph.D program in Algorithms, Combinatorics, and Optimization (ACO). This program is the first of its kind in the United States. It is administered jointly by the Tepper School of Business (Operations Research group), the Computer Science Department (Algorithms and Complexity group), and the Department of Mathematical Sciences (Discrete Mathematics group).

The mathematics used by computer scientists and operations researchers overlap to a large extent. The boundaries between Operations Research and Computer Science have become blurred. Important new theories and whole fields, like polyhedral combinatorics, have been and are being developed jointly by computer scientists, operations researchers, and applied mathematicians who consider themselves a little bit of both. Presentations of new results on graphs and matroid theory can be heard at Operations Research conferences, while papers on linear programming, network flows, and matchings in graphs are frequently presented at Computer Science conferences. The mathematical content of the papers has become greater and more diverse. Yet, in spite of this, few Ph.D students graduate with an equally solid knowledge of all three areas.

The Ph.D program in Algorithms, Combinatorics, and Optimization at Carnegie Mellon is intended to fill this gap. The program brings together the study of the mathematical structure of discrete objects and the design and analysis of algorithms in areas such as graph theory, combinatorial optimization, integer programming, polyhedral theory, computational algebra, geometry, and number theory.

Below is the list of expert faculty who will serve in the key areas of teaching within the ACO program.

Mathematical Sciences Faculty

Thomas Bohman

Extremal Combinatorics...


Boris Bukh

Combinatorial geometry, combinatorial number theory...


Florian Frick

Geometric and topological methods...


Alan Frieze

Average case analysis of algorithms, combinatorics...


Po-Shen Loh

Probabilistic and Extremal Combinatorics, and applications to Theoretical Computer Science...


Wesley Pegden

Combinatorics, Abelian Sandpile problem...


Prasad Tetali

Markov chains, Isoperimetry and Functional Analysis, Combinatorics...


Konstantin Tikhomirov

Discrete Probability, Combinatorics...


Michael Young

Discrete Mathematics, primarily Graph Theory and Combinatorics...


Computer Science Faculty

Nina Balcan

Machine learning, computational aspects in economics and game theory, algorithms...


Guy Blelloch

Parallel algorithms and languages...


Mor Harchol-Balter

Queueing theory, stochastic modeling, probability theory, heavy-tailed workloads, Web servers, networking...


Ryan O'Donnell

Complexity theory, analysis of boolean functions, approximation hardness...


Steven Rudich

Complexity theory, cryptography, combinatorics...


Tuomas Sandholm

Market design, game theory, optimization (integer programming, search, stochastic optimization...)


Daniel Sleator

Data structures, algorithms, parsing...


Operations Research Faculty

Fatma Kılınç-Karzan

Convex optimization, large-scale algorithms, decision making under uncertainty...


Benjamin Moseley

Design, analysis and evaluation of algorithms...


Javier Peña

Theory and algorithms for convex optimization, numerical analysis...


R. Ravi

Approximation algorithms, combinatorial optimization, computational biology...


Michael Trick

Computational integer and combinatorial optimization, applications in sports and the social sciences...


Willem Van Hoeve

Combinatorial optimization; constraint programming; mathematical programming; integration of constraint programming and mathematical programming...