Vijay V. Vazirani

Distinguished Professor
Computer Science Department
University of California, Irvine

Director, ACO Center @ UCI

Ph.D., University of California, Berkeley
S.B., Massachusetts Institute of Technology

Three Recent Talks:

1). Online Bipartite Matching and Adwords
Talk at Institute of Advanced Studies, Princeton, March 2022..

2). A Theory of Alternating Paths and Blossoms, from the Perspective of Minimum Length Two-talk sequance, Simons Institute, October, 2023.

3). LP-Duality and the Cores of Games
Online and Matching-Based Market Design, Simons Institute Workshop, October, 2023

My Picture

Some Interesting Asides:

1). My father's books

2). John von Neumann Theory Prize Citation.

3). TCS: Looking into the Future

4). A worthy cause

Research Interests

Algorithmic problems in mathematical economics and game theory, design of efficient exact and approximation algorithms, computational complexity theory.


1). Approximation Algorithms, Springer-Verlag, Berlin, 2001.
Preface, Table of Contents, and Chapter 1.

2). Algorithmic Game Theory, Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay V. Vazirani, editors, Cambridge University Press, Cambridge, 2007.
Non-printable version on the web and DIMAP Workshop (Warwick University) introducing the book.

3). Online and Matching-Based Market Design, Federico Echenique, Nicole Immorlica and Vijay V. Vazirani, editors, Cambridge University Press, Cambridge, 2023.
Available for free download here. The password is OMBMD_CUP

Selected Recent Papers

Matching-Based Papers

  • ``A Theory of Alternating Paths and Blossoms, from the Perspective of Minimum Length'', To appear in Math of Operations Research.
    Two-talk sequance, Simons Institute, October, 2023.

  • ``The Assignment Game: New Mechanisms for Equitable Core Imputations'', arXiv, 2024.

  • ``Cardinal-Utility Matching Markets: The Quest for Envy-Freeness, Pareto-Optimality, and Efficient Computability'', with T. Trobst, ACM EC, 2024.

  • ``LP-Duality Theory and the Cores of Game'', arXiv, 2023.

  • ``The Investment Management Game: Extending the Scope of the Notion of Core'', SAGT, 2024.

  • "Towards a Practical, Budget-Oblivious Algorithm for the Adwords Problem under Small Bids", FSTTCS, 2023.

  • ``The General Graph Matching Game: Approximate Core'', Games and Economic Behavior, vol 132 (2022).

  • ''The Stable Matching Lattice under Changed Preferences, and Associated Algorithms'', with R. Gangam, T. Mai and N. Raju, arXiv, 2023.

  • ``Cores of Games via Total Dual Integrality, with Applications to Perfect Graphs and Polymatroids'', arXiv, 2022.

  • ``New Characterizations of Core Imputations of Matching and b-Matching Games'', FSTTCS, 2022.

  • ''A Structural and Algorithmic Study of Stable Matching Lattices of ``Nearby'' Instances, with Applications'', with R. Gangam, T. Mai and N. Raju, FSTTCS, 2022.

  • ``Online Bipartite Matching and Adwords'', Mathematical Foundations of Computer Sceince, 2022.

  • ``Combinatorial Algorithms for Matching Markets via Nash Bargaining: One-Sided, Two-Sided and Non-Bipartite*'', with I. Panageas and T. Trobst, arXiv, 2021.

  • ``Nash-Bargaining-Based Models for Matching Markets: One-Sided and Two-Sided; Fisher and Arrow-Debrew'', with M. Hosseini, ITCS, 2022.

  • ``One-Sided Matching Markets with Endowments: Equilibria and Algorithms'', with J. Garg and T. Trobst, AAMAS, 2022.

  • ``An Extension of the Birkhoff-von Neumann Theorem to Non-Bipartite Graphs'', arXiv, 2020.

  • ``Stability-Preserving, Time-Efficient Mechanisms for School Choice in Two Rounds'', with K. Gajulapalli,, J. Liu and T. Mai, FSTTCS, 2020.

  • ``Computational Complexity of the Hylland-Zeckhauser Scheme for One-Sided Matching Markets'', with M. Yannakakis, ITCS, 2021.

  • ``A Real Polynomial for Bipartite Graph Minimum Weight Perfect Matchings'', with T. Trobst, Information Processing Letters, 2022.

  • ``Matching is as Easy as the Decision Problem, in the NC Model'', with N. Anari, ITCS, 2020.

  • ``Planar Graph Perfect Matching is in NC''. with N. Anari, FOCS, 2018. Journal of ACM 67(4), 2020.

  • ``NC Algorithms for Perfect Matching and Maximum Flow in One-Crossing-Minor-Free Graphs''. with D. Eppstein, SIAM J. COMPUT 50(3), 2021.

  • ``Finding Stable Matchings that are Robust to Errors in the Input''. with T. Mai, ESA, 2018.

    Algorithms for Markets and Bargaining

  • ``Nash Social Welfare for Indivisible Items under Separable, Piecewise-Linear Concave Utilities''. with N. Anari, T. Mai and S. Oveis Gharan, SODA, 2018.

  • ``A Performance-Based Scheme for Pricing Resources in the Cloud''. with K. Jain and T. Mai, WINE, 2017.

  • ``Settling the Complexity of Arrow-Debreu Markets under Leontief and PLC Utilities, using the Classes FIXP and ∃R''. with J. Garg, R. Mehta and S. Yazdanbod, STOC, 2017.

  • ``Convex Program Duality, Fisher Markets, and Nash Social Welfare''. with R. Cole, N. Devanur, V. Gkatzelis, K. Jain, T. Mai and S. Yazdanbod, ACM EC, 2017.

  • ``A New Class of Combinatorial Markets with Covering Constraints: Algorithms and Applications''. with N. Devanur, J. Garg, R. Mehta and S. Yazdanbod, SODA, 2017.

  • ``Allocation of Divisible Goods under Lexicographic Preferences'', with L. Schulman, FSTTCS (2015).

  • ``Dichotomies in Equilibrium Computation, and Complementary Pivot Algorithms for a New Class of Non-Separable Utility Functions'', with J. Garg and R. Mehta, STOC (2014).

  • ``An Incentive Compatible, Efficient Market for Air Traffic Flow Management, with R. Mehta, Theoretical Computer Science (2020).

  • ``On Computability of Equilibria in Markets with Production'', with J. Garg, SODA (2014).

  • ``A Complementary Pivot (Practical) Algorithm for Markets Under Separable, Piecewise-Linear Concave Utilities'', with J. Garg, R. Mehta and M. Sohoni, STOC (2012).

  • ``The Notion of a Rational Convex Program, and an Algorithm for the Arrow-Debreu Nash Bargaining Game'', Journal of ACM, vol. 59(2) (2012).

  • ``Market Equilibrium under Separable, Piecewise-Linear, Concave Utilities'', with M. Yannakakis, Journal of ACM, vol. 58(3) (2011).

  • ``Equilibrium Pricing of Semantically Substitutable Digital Goods'', with K. Jain, in arXiv, (2012).

  • ``How Many Tiers? Pricing in the Internet Transit Market'', with V. Valancius, C. Lumezanu, N. Feamster and R. Johari, SIGCOMM (2011).

  • ``Non-Separable, Concave Utilities are Easy -- in a Perfect Price Discrimination Market Model'', SIAM J. Discrete Math, 27(1) (2013).

  • ``Rational Convex Programs and Efficient Algorithms for 2-Player Nash and Nonsymmetric Bargaining Games'', SIAM J. Discrete Math, 26(3) (2012).

  • ``A Perfect Price Discrimination Market Model with Production, and a Rational Convex Program for it'', with G. Goal, Math of Operations Research, 36: 762-782 (2011).

  • ``Continuity Properties of Equilibrium Prices and Allocations in Linear Fisher Markets'', with N. Megiddo, WINE (2007).

  • ``Spending Constriant Utilities, with Applications to the Adwords Market'', Math of Operations Research 35(2), 2010.

  • ``New Results on Rationality and Strongly Polynomial Solvability in Eisenberg-Gale Markets with Two Agents'', with D. Chakrabarty and N. Devanur, SIAM J. Discrete Math, 24(3), 2010.

  • ``Eisenberg-Gale Markets: Algorithms and Game-Theoretic Properties'', with K. Jain, Games and Economic Behavior, 70(1), 2010.

  • ``Adwords and Generalized Online Matching'', with A. Mehta, A. Saberi and U. Vazirani, Journal of ACM 54(5), 2007.
    SIAM News article by Sara Robinson on this work.

  • ``Market Equilibria for Homothetic, Quasi-Concave Utilities and Economies of Scale in Procudtion'', with K. Jain and Y. Ye, SODA (2005).

  • ``Rate Control as a Market Equilibrium'', with F. P. Kelly, unpublished note (2002).

  • ``Market Equilibrium via a Primal-Dual Algorithm for a Convex Program'', with N. Devanur, C. Papadimitriou, and A. Saberi, Journal of ACM, vol. 55(5) (2008).

    Other Recent Papers

    1. ``Cycles in Zero-Sum Differential Games and Biological Diversity'', with T. Mai, M. Mihail, I. Panageas, W. Ratcliff and P. Yunker, ACM EC, 2018.

    2. ``Mutation, Sexual Reproduction and Survival in Dynamic Environments'', with R. Mehta, I. Panageas, G. Piliouras and P. Tetali, ITCS, 2017.

    3. ``Settling Some Open Problems on 2-Player Symmetric Nash Equilibria'', with R. Mehta and S. Yazdanbod, SAGT (2015).

    4. ``ETR-Completeness for Decision Versions of Multi-Player (Symmetric) Nash Equilibria'', with J. Garg, R. Mehta and S. Yazdanbod, ICALP (2015).

    5. ``New Geometry-Inspired Relaxations and Algorithms for the Metric Steiner Tree Problem'', with D. Chakrabarty and N. Devanur, Math Programming, Series A (2009).

    6. ``Solvency Games'', with N. Berger, N. Kapur, and L. Schulman, FSTTCS 2008.

    7. ``Design is as Easy as Optimization'', with D. Chakrabarty and A. Mehta, SIAM Journal on Discrete Math, 24(1) (2010).

    8. ``Equitable Cost Allocations via Primal-Dual-Type Algorithms'', with K. Jain, SIAM Journal on Computing, 38(1) (2008).

    9. ``Diversity in Times of Adversity: Probabilistic Strategies in Microbial Survival Games'', with D. Wolf and A. Arkin, Journal of Theoretical Biology, vol. 234, 2005.
      Reviewed in Faculty of 1000.

    10. ``A Microbial Modified Prisoner's Dilemma Game: How Frequency-Dependent Selection can Lead to Random Phase Variation'', with D. Wolf and A. Arkin, Journal of Theoretical Biology, vol. 234, 2005.

    11. ``The Spending Constraint Model for Market Equilibrium: Algorithmic, Existence and Uniqueness Results'', with N. Devanur, STOC 2004.

    12. ``On the Capacity of Multiple Unicast Sessions in Unidrected Networks'', with K. Jain, R. Yeung and G. Yuval, ISIT 2005.

    13. ``Improved Simulated Annealing Algoirthm for the Permanent and Combinatorial Counting Problems'', with I. Bezakova, D. Stefankovic and E. Vigoda, SIAM Journal of Computing, 37(5) (2008) 1429 -1454.

    14. ``A stochastic process on the hypercube with applications to peer-to-peer networks'', with M. Adler, E. Halperin, and R. M. Karp, Proc. STOC 2003.

    15. ``Greedy Facility Location Algorithms Analyzed using Dual Fitting with Factor-Revealing LP'', with K. Jain, M. Mahdian, E. Markakis, and A. Saberi, Journal of ACM, 50(6) (2003), 795-824.

    16. ``A computationally motivated definition of parametric estimation and its applications to the Gaussian distribution'', with L. J. Schulman, Combinatorica 25(4) (2005) 465-486.

    17. ``Applications of Approximation Algorithms to Cooperative Games'', with K. Jain, Proc. STOC 2001.

    18. ``Approximation Algorithms for Metric Facility Location and k-Median Problems Using the Primal-Dual Schema and Lagrangian Relaxation'', with K. Jain, Journal of ACM, Vol. 48 (2001) 274-296.

    19. ``A Graph Theoretic Approach to Software Watermarking'', with R. Venkatesan and S. Sinha, 4th International Information Hiding Workshop, Pittsburgh (2001).

    20. ''An optimal algorithm for on-line bipartite matching'', with R. Karp and U. Vazirani, STOC (1990).

    21. ``Pfaffian Orientations, 0/1 Permanents, and Even Cycles in Directed Graphs.'', with M. Yannakakis, Discrete and Applied Mathematics, 25. (1989).

    Other Selected Papers: Click here

    Selected Talks

    Online Bipartite Matching and Adwords
    Talk at Institute of Advanced Studies, Princeton, March 2022..

    New Insights into Shapley-Shubik
    Talk at Harvard University, April 2022..

    TAU Theory-Fest, Plenary Session, 2019:

    Matching is as Easy as the Decision Problem, in the NC Model

    Simons Institute Richard M. Karp Distinguished Lecture, 2019: Algorithmic Opportunities in Matching Markets.

    Simons Institute, 2018: Google's AdWords Market: How Theory Influenced Practice.

    University of Washington TV, 2010: The "Invisible Hand of the Market": Algorithmic Ratification and the Digital Economy.

    Two talks for the algorithmically inclined on
    ``Combinatorial Algorithms for Convex Programs Capturing Market Equilibria and Nash Bargaining Solutions''

    Egervary Research Group on Combinatorial Optimization, Budapest, Hungary, September 2009.

    1) The Problems
    2) Algorithms

    ``Nash Bargaining via Flexible Budget Markets'' talk ppt
    Youtube, Google Research, September 2008.

    ``New Market Models and Algorithms'' talk ppt
    Webcast from Microsoft Research, May 2006.
    ACO Distinguished Lecture, April 2006.

    ``Markets and the Primal-Dual Paradigm'' talk ppt
    Keynote address, DIMAP Workshop, Warwick University, March 2007.
    MS&E Colloquium (Distinguished lecture), Stanford University, May 2007.
    Plenary talk, WINE, San Diego, December 2007.

    Past and Present Ph.D. Students

      Mark Krentel
      Samir Khuller
      Naveen Garg
      Kamal Jain
      Ion Mandoiu
      Amin Saberi
      Aranyak Mehta
      Nikhil R. Devanur
      Deeparnab Chakrabarty
      Gagan Goel
      Chinmay Karande
      Lei Wang
      Pushkar Tripathi
      Sadra Yazdanbod
      Tung Mai
      Thorben Trobst
      Rohith Reddy Gangam
      Parnian Shahkar
      Nikolas Patris

    Past and Present Postdocs

      Gagan Goel
      Laszlo Vegh
      Ruta Mehta
      Jugal Garg
      Tung Mai

    Selected Workshops and Programs Co-organized

    Selected Blog Posts

    Department of Computer Science
    Donald Bren School of Information and Computer Sciences
    University of California, Irvine
    4032 Donald Bren Hall
    Irvine, CA 92697-3435
    vazirani AT ics DOT uci DOT edu