David D. Gamarnik

About

David Gamarnik is a Professor of Operations Research at the MIT Sloan School of Management. His research interests include discrete probability and random structures, algorithms and combinatorial optimization, statistics and machine learning, quantum computing and quantum information science, as well as stochastic processes and queueing theory. He received his B.A. in Mathematics from New York University in 1993 and his Ph.D. in Operations Research from MIT in 1998. Prior to joining MIT as a faculty member in 2005, he was a research staff member at IBM T. J. Watson Research Center from 1997 to 2005. Gamarnik is a fellow of the American Mathematical Society, the Institute for Operations Research and the Management Sciences, and the Institute for Mathematical Statistics. His notable contributions include co-authoring a textbook on queueing theory, serving as an area editor for the Mathematics of Operations Research journal, and delivering numerous lectures and tutorials on topics such as classical and quantum computing in random structures, the overlap gap property, and algorithmic hardness in random structures. He has received awards such as the Erlang Prize and the Best Publication Award from the Applied Probability Society of INFORMS, and has been recognized as a finalist in the Franz Edelman Prize competition of INFORMS.

Research topics

• Computer Science
• Mathematics
• Artificial Intelligence
• Algorithm
• Combinatorics
• Machine Learning
• Quantum mechanics
• Physics
• Theoretical computer science
• Mathematical optimization

Selected publications

• The overlap gap property: A topological barrier to optimizing over random structures

  Proceedings of the National Academy of Sciences · 2021 · 94 citations

  1st authorCorresponding

  -hardness is lacking. A new approach for algorithmic intractability in random structures is described in this article, which is based on the topological disconnectivity property of the set of pairwise distances of near-optimal solutions, called the Overlap Gap Property. The article demonstrates how this property 1) emerges in most models known to exhibit an apparent algorithmic hardness; 2) is consistent with the hardness/tractability phase transition for many models analyzed to the day; and, im…

  DOI

• The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: A Typical Case

  arXiv (Cornell University) · 2020 · 89 citations

  The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with bounded degree, with p small enough, measurements of distant qubits in the state output by the QAOA give uncorrelated results. We focus on finding big independent sets in random graphs with dn/2 edges keeping d fixed and n large. Using the Overlap Gap Property of al…

  DOI

• The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: Worst Case Examples

  arXiv (Cornell University) · 2020 · 55 citations

  The Quantum Approximate Optimization Algorithm can be applied to search problems on graphs with a cost function that is a sum of terms corresponding to the edges. When conjugating an edge term, the QAOA unitary at depth p produces an operator that depends only on the subgraph consisting of edges that are at most p away from the edge in question. On random d-regular graphs, with d fixed and with p a small constant time log n, these neighborhoods are almost all trees and so the performance of the…

  DOI

• Algorithmic obstructions in the random number partitioning problem

  The Annals of Applied Probability · 2023-12-01 · 14 citations

  articleOpen access1st authorCorresponding

  We consider the algorithmic problem of finding a near-optimal solution for the number partitioning problem (NPP). This problem appears in many practical applications, including the design of randomized controlled trials, multiprocessor scheduling, and cryptography. It is also of theoretical significance. The NPP possesses a so-called statistical-to-computational gap: when its input X has distribution N(0,In), the optimal value of the NPP is Θ(n2−n) w.h.p., whereas the best-known polynomial-time…

  PublisherOA PDFDOI

• The landscape of the planted clique problem: Dense subgraphs and the overlap gap property

  The Annals of Applied Probability · 2024-08-01 · 5 citations

  article1st authorCorresponding

  We study the computational-statistical gap of the planted clique problem, where a clique of size k is planted in an Erdős–Rényi graph G(n,12). The goal is to recover the planted clique vertices by observing the graph. It is known that the clique can be recovered as long as k≥(2+ϵ)logn for any ϵ>0, but no polynomial-time algorithm is known for this task unless k=Ω(n). Following a statistical-physics inspired point of view, as a way to understand the nature of this computational-statistical gap, w…

  PublisherDOI

Recent grants

• AF: Small: Low-Degree Methods for Optimization in Random Structures. Power and Limitations

  NSF · $531k · 2023–2026

• Statistical Physics Methods and Algorithmic Applications in Graphical Games and Combinatorial Optimization

  NSF · $337k · 2010–2013

• Inference in High-Dimensional Statistical Models: Algorithmic Tractability and Computational Barriers

  NSF · $200k · 2020–2023

Frequent coauthors

• Eren C. Kızıldağ

  Columbia University

  21 shared

• Ilias Zadik

  New York University

  20 shared

• Devavrat Shah

  19 shared

• Prasad Tetali

  17 shared

• Dimitris Bertsimas

  16 shared

• David A. Goldberg

  Cornell University

  15 shared

• Dmitriy Katz

  15 shared

• Madhu Sudan

  Harvard University Press

  13 shared

Awards & honors

• Erlang Prize
• Best Publication Award from the Applied Probability Society…
• Fellow of the Institute for Mathematical Statistics (IMS) (2…
• INFORMS Fellow (2021)
• Fellow of the American Mathematical Society (AMS) (2022)

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