Statistical Physics and Algorithms (Invited Talk)
The field of randomized algorithms has benefitted greatly from insights from statistical physics. We give examples in two distinct settings. The first is in the context of Markov chain Monte Carlo algorithms, which have become ubiquitous across science and engineering as a means of exploring large configuration spaces. One of the most striking discoveries was the realization that many natural Markov chains undergo phase transitions, whereby they are efficient for some parameter settings and then suddenly become inefficient as a parameter of the system is slowly modified. The second is in the context of distributed algorithms for programmable matter. Self-organizing particle systems based on statistical models with phase changes have been used to achieve basic tasks involving coordination, movement, and conformation in a fully distributed, local setting. We briefly describe these two settings to demonstrate how computing and statistical physics together provide powerful insights that apply across multiple domains.
Markov chains
mixing times
phase transitions
programmable matter
Theory of computation~Random walks and Markov chains
Mathematics of computing~Stochastic processes
Theory of computation~Self-organization
1:1-1:6
Invited Talk
Funded in part by NSF awards CCF-1526900, CCF-1637031, CCF-1733812 and ARO MURI award #W911NF-19-1-0233.
Dana
Randall
Dana Randall
School of Computer Science, Georgia Institute of Technology, Atlanta, GA 30332-0765, USA
10.4230/LIPIcs.STACS.2020.1
Marta Andrés Arroyo, Sarah Cannon, Joshua J. Daymude, Dana Randall, and Andréa W. Richa. A stochastic approach to shortcut bridging in programmable matter. In DNA Computing and Molecular Programming, DNA23, pages 122-138, 2017.
Marta Andrés Arroyo, Sarah Cannon, Joshua J. Daymude, Dana Randall, and Andréa W. Richa. A stochastic approach to shortcut bridging in programmable matter. Natural Computing, 17(4):723-741, 2018.
Akhilest K. Arora and Raj Rajagopalan. Applications of colloids in studies of phase transitions and patterning of surfaces. Current Opinion in Colloid & Interface Science, 2(4), 1997.
R. J. Baxter, I. G. Enting, and S. K. Tsang. Hard-square lattice gas. Journal of Statistical Physics, 22:465-489, 1980.
Prateek Bhakta, Sarah Miracle, and Dana Randall. Clustering and mixing times for segregation models on ℤ². In Proceedings of the 25th ACM/SIAM Symposium on Discrete Algorithms, (SODA), 2014.
Nayantara Bhatnagar and Dana Randall. Simulated tempering and swapping on mean-field models. Journal of Statistical Physics, 164(3):495-530, 2016.
Antonio Blanca, Yuxuan Chen, David Galvin, Dana Randall, and Prasad Tetali. Phase coexistence for the hard-core model on ℤ². Combinatorics, Probability and Computing, pages 1-22, 2018.
Antonio Blanca, David Galvin, Dana Randall, and Prasad Tetali. Coexistence and slow mixing for the hard-core model on ℤ². In Approximation, Randomization and Combinatorial Optimization (APPROX/RANDOM), volume 8096, pages 379-394, 2013.
Bela Bollobas. The evolution of random graphs. Transactions of the American Mathematical Society, 286(1):257-274, 1984.
Christian Borgs, Jennifer T. Chayes, Jeong Han Kim, Alan Frieze, Prasad Tetali, Eric Vigoda, and Van Ha Vu. Torpid mixing of some Monte Carlo Markov chain algorithms in statistical physics. In Proceedings of the 40th Annual Symposium on Foundations of Computer Science, FOCS '99, pages 218-229, Washington, DC, USA, 1999. IEEE Computer Society.
Sarah Cannon, Joshua J. Daymude, Cem Gökmen, Dana Randall, and Andréa W. Richa. A local stochastic algorithm for separation in heterogeneous self-organizing particle systems. In Approximation, Randomization and Combinatorial Optimization (APPROX/RANDOM), pages 54:1-54:22, 2019.
Sarah Cannon, Joshua J. Daymude, Dana Randall, and Andréa W. Richa. A Markov chain algorithm for compression in self-organizing particle systems. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC '16, pages 279-288, New York, NY, USA, 2016. ACM.
Zahra Derakhshandeh, Robert Gmyr, Andréa W. Richa, Christian Scheideler, and Thim Strothmann. An algorithmic framework for shape formation problems in self-organizing particle systems. In Proceedings of the Second Annual International Conference on Nanoscale Computing and Communication, NANOCOM '15, pages 21:1-21:2, 2015.
Roland L. Dobrushin. The problem of uniqueness of a gibbsian random field and the problem of phase transitions. Functional Analysis and Its Applications, 2:302-312, 1968.
Bahnisikha Dutta, Shengkai Li, Sarah Cannon, Joshua J. Daymude, Enes Aydin, Andrea W. Richa, Daniel I. Goldman, and Dana Randall. Programming robot collecitves using mechanics-induced phase changes, 2020. (In preparation).
Sacha Friedli and Yvan Velenik. Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction. Cambridge University Press, Cambridge, 2017.
Vivek K. Gore and Mark R. Jerrum. The Swendsen-Wang process does not always mix rapidly. Journal of Statistical Physics, 97(1):67-86, 1999.
Tyler Helmuth, Will Perkins, and Guus Regts. Algorithmic pirogov-sinai theory. In Proceedings of the 51st Annual ACM Symposium on the Theory of Computing, pages 1009-1020, 2019.
Svante Janson, Donald Knuth, Tomasz Luczak, and Boris Pittel. The birth of the giant component. Random Structures and Algorithms, 4(3):231-358, 1993.
Mark R. Jerrum, Alistair Sinclair, and Eric Vigoda. A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries. Journal of the ACM, 51:671-697, 2004.
Sarah Miracle, Dana Randall, and Amanda Pascoe Streib. Clustering in interfering binary mixtures. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX '11, RANDOM '11, pages 652-663, 2011.
Gerald H. Pollack and Wei-Chun Chin (Eds.), editors. Phase Transitions in Cell Biology. Springer International Publishing, 2008.
Chris R. Reid, Matthew J. Lutz, Scott Powell, Albert B. Kao, Iain D. Couzin, and Simon Garnier. Army ants dynamically adjust living bridges in response to a cost-benefit trade-off. Proceedings of the National Academy of Sciences, 112(49):15113-15118, 2015.
William Savoie, Sarah Cannon, Joshua J. Daymude, Ross Warkentin, Shengkai Li, Andréa W. Richa, Dana Randall, and Daniel I. Goldman. Phototactic supersmarticles. Artificial Life and Robotics, 23(4):459-468, 2018.
Thomas C. Schelling. Models of segregation. American Economic Review, 59(2):488-493, 1969.
Alistair Sinclair, Piyush Srivastava, Daniel Stefankovic, and Yintong Yin. Spatial mixing and the connective constant: Optimal bounds. Probabability Theory Relatated Fields, 168(1-2):153-197, 2017.
Leslie Valiant. The complexity of computing the permanent. Theoretical Computer Science, 8:189-201, 1979.
Jian-Sheng Wang and Robert H. Swendsen. Nonuniversal critical dynamics in monte carlo simulations. Physics Review Letters, 58(2):86-88, 1987.
Dana Randall
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