Sponsored by IEEE Computer Society Technical Committee On

Total Page:16

File Type:pdf, Size:1020Kb

Sponsored by IEEE Computer Society Technical Committee On Reviewers Dorit Aharonov Uriel Feige Ralf Klasing R. Rajaraman Susanne Albers Eldar Fischer Phil Klein Dana Randall Eric Allender Lance Fortnow Jon Kleinberg Satish Rao Noga Alon Ehud Friedgut M. Klugerman Ran Raz Nina Amenta Alan Frieze Pascal Koiran A. Razborov Lars Arge Hal Gabow Elias Koutsoupias Bruce Reed Hagit Attiya Naveen Garg Matthias Krause Oded Regev Yossi Azar Leszek Oliver Kullmann Omer Reingold Laci Babai Gasieniec Andre Kundgen Dana Ron David Barrington Ashish Goel Orna Ronitt Rubinfeld A. Barvinok Michel Kupferman Steven Rudich Saugata Basu Goemans Eyal Kushilevitz Amit Sahai Paul Beame Paul Goldberg Arjen Lenstra Cenk Sahinalp Jozsef Beck Oded Goldreich Nati Linial Michael Saks Mihir Bellare M. Grigni Philip Long Raimund Seidel Petra Berenbrink Leo Guibas Dominic Mayers David Shmoys Dan Boneh Vassos David Amin Shokrollahi Julian Bradfield Hadzilacos McAllester Alistair Sinclair Nader Bshouty Peter Hajnal M. Danny Sleator Peter Buergisser Ramesh Mitzenmacher Warren Smith Hariharan Ran Canetti Michael Molloy Joel Spencer George Havas N. Cesa-Bianchi Yoram Moses Dan Spielman Xin He Bernard Ian Munro Aravind Chazelle Dan Hirschberg S. Muthukrishnan Srinivasan Ed Coffman Mike Hutton Ashwin Nayak Angelika Steger Edith Cohen Neil Immerman Peter Neumann Cliff Stein Richard Cole Russell Shmuel Onn Alexander Impagliazzo Steve Cook Rafail Ostrovsky Stolyar Piotr Indyk Gene Janos Pach Martin Strauss Cooperman Yuval Ishai C. Bernd Sturmfels Derek Corneil Andreas Jakoby Papadimitriou Benny Sudakov Felipe Cucker Mark Jerrum Boaz Patt- Madhu Sudan Sanjoy Erich Kaltofen Shamir Ondrej Sykora Dasgupta Ravi Kannan David Peleg Christian Luc Devroye Sampath Enoch Peserico Szegedy Shlomi Dolev Kannan Erez Petrank Amnon Ta-Shma Jeff Edmonds Haim Kaplan Maurizio Pizzonia E. Ternovskaia Noam Elkies George Pavel Pudlak Prasad Tetali Karakostas Ioannis Emiris Yuval Rabani Denis Therien Richard Karp David Eppstein Uri Rabinovich Mikkel Thorup Leonid William Evans Charlie Rackoff Alexandre Tiskin Khachiyan M. Farach- P. Raghavan Andrew Tomkins Sanjeev Khanna Colton S. Rajagopalan Luca Trevisan Valerie King Chris Umann Vijay Vazirani Eric Vigoda Peter Winkler Alisdair Urquhart Boban Uzi Vishkin G. Woeginger Mahesh V Velickovich Nicolai Vorobjov Neal Young Salil Vadhan Santosh John Watrous Uri Zwick Moshe Vardi Vempala Avi Wigderson .
Recommended publications
  • Reproducibility and Pseudo-Determinism in Log-Space
    Reproducibility and Pseudo-determinism in Log-Space by Ofer Grossman S.B., Massachusetts Institute of Technology (2017) Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 c Massachusetts Institute of Technology 2020. All rights reserved. Author...................................................................... Department of Electrical Engineering and Computer Science May 15, 2020 Certified by.................................................................. Shafi Goldwasser RSA Professor of Electrical Engineering and Computer Science Thesis Supervisor Accepted by................................................................. Leslie A. Kolodziejski Professor of Electrical Engineering and Computer Science Chair, Department Committee on Graduate Students 2 Reproducibility and Pseudo-determinism in Log-Space by Ofer Grossman Submitted to the Department of Electrical Engineering and Computer Science on May 15, 2020, in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science Abstract Acuriouspropertyofrandomizedlog-spacesearchalgorithmsisthattheiroutputsareoften longer than their workspace. This leads to the question: how can we reproduce the results of a randomized log space computation without storing the output or randomness verbatim? Running the algorithm again with new
    [Show full text]
  • Computational Learning Theory: New Models and Algorithms
    Computational Learning Theory: New Models and Algorithms by Robert Hal Sloan S.M. EECS, Massachusetts Institute of Technology (1986) B.S. Mathematics, Yale University (1983) Submitted to the Department- of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 1989 @ Robert Hal Sloan, 1989. All rights reserved The author hereby grants to MIT permission to reproduce and to distribute copies of this thesis document in whole or in part. Signature of Author Department of Electrical Engineering and Computer Science May 23, 1989 Certified by Ronald L. Rivest Professor of Computer Science Thesis Supervisor Accepted by Arthur C. Smith Chairman, Departmental Committee on Graduate Students Abstract In the past several years, there has been a surge of interest in computational learning theory-the formal (as opposed to empirical) study of learning algorithms. One major cause for this interest was the model of probably approximately correct learning, or pac learning, introduced by Valiant in 1984. This thesis begins by presenting a new learning algorithm for a particular problem within that model: learning submodules of the free Z-module Zk. We prove that this algorithm achieves probable approximate correctness, and indeed, that it is within a log log factor of optimal in a related, but more stringent model of learning, on-line mistake bounded learning. We then proceed to examine the influence of noisy data on pac learning algorithms in general. Previously it has been shown that it is possible to tolerate large amounts of random classification noise, but only a very small amount of a very malicious sort of noise.
    [Show full text]
  • Information Theory Methods in Communication Complexity
    INFORMATION THEORY METHODS IN COMMUNICATION COMPLEXITY BY NIKOLAOS LEONARDOS A dissertation submitted to the Graduate School—New Brunswick Rutgers, The State University of New Jersey in partial fulfillment of the requirements for the degree of Doctor of Philosophy Graduate Program in Computer Science Written under the direction of Michael Saks and approved by New Brunswick, New Jersey JANUARY, 2012 ABSTRACT OF THE DISSERTATION Information theory methods in communication complexity by Nikolaos Leonardos Dissertation Director: Michael Saks This dissertation is concerned with the application of notions and methods from the field of information theory to the field of communication complexity. It con- sists of two main parts. In the first part of the dissertation, we prove lower bounds on the random- ized two-party communication complexity of functions that arise from read-once boolean formulae. A read-once boolean formula is a formula in propositional logic with the property that every variable appears exactly once. Such a formula can be represented by a tree, where the leaves correspond to variables, and the in- ternal nodes are labeled by binary connectives. Under certain assumptions, this representation is unique. Thus, one can define the depth of a formula as the depth of the tree that represents it. The complexity of the evaluation of general read-once formulae has attracted interest mainly in the decision tree model. In the communication complexity model many interesting results deal with specific read-once formulae, such as disjointness and tribes. In this dissertation we use information theory methods to prove lower bounds that hold for any read-once ii formula.
    [Show full text]
  • Computational Complexity Computational Complexity
    In 1965, the year Juris Hartmanis became Chair Computational of the new CS Department at Cornell, he and his KLEENE HIERARCHY colleague Richard Stearns published the paper On : complexity the computational complexity of algorithms in the Transactions of the American Mathematical Society. RE CO-RE RECURSIVE The paper introduced a new fi eld and gave it its name. Immediately recognized as a fundamental advance, it attracted the best talent to the fi eld. This diagram Theoretical computer science was immediately EXPSPACE shows how the broadened from automata theory, formal languages, NEXPTIME fi eld believes and algorithms to include computational complexity. EXPTIME complexity classes look. It As Richard Karp said in his Turing Award lecture, PSPACE = IP : is known that P “All of us who read their paper could not fail P-HIERARCHY to realize that we now had a satisfactory formal : is different from ExpTime, but framework for pursuing the questions that Edmonds NP CO-NP had raised earlier in an intuitive fashion —questions P there is no proof about whether, for instance, the traveling salesman NLOG SPACE that NP ≠ P and problem is solvable in polynomial time.” LOG SPACE PSPACE ≠ P. Hartmanis and Stearns showed that computational equivalences and separations among complexity problems have an inherent complexity, which can be classes, fundamental and hard open problems, quantifi ed in terms of the number of steps needed on and unexpected connections to distant fi elds of a simple model of a computer, the multi-tape Turing study. An early example of the surprises that lurk machine. In a subsequent paper with Philip Lewis, in the structure of complexity classes is the Gap they proved analogous results for the number of Theorem, proved by Hartmanis’s student Allan tape cells used.
    [Show full text]
  • The Communication Complexity of Interleaved Group Products
    The communication complexity of interleaved group products W. T. Gowers∗ Emanuele Violay April 2, 2015 Abstract Alice receives a tuple (a1; : : : ; at) of t elements from the group G = SL(2; q). Bob similarly receives a tuple (b1; : : : ; bt). They are promised that the interleaved product Q i≤t aibi equals to either g and h, for two fixed elements g; h 2 G. Their task is to decide which is the case. We show that for every t ≥ 2 communication Ω(t log jGj) is required, even for randomized protocols achieving only an advantage = jGj−Ω(t) over random guessing. This bound is tight, improves on the previous lower bound of Ω(t), and answers a question of Miles and Viola (STOC 2013). An extension of our result to 8-party number-on-forehead protocols would suffice for their intended application to leakage- resilient circuits. Our communication bound is equivalent to the assertion that if (a1; : : : ; at) and t (b1; : : : ; bt) are sampled uniformly from large subsets A and B of G then their inter- leaved product is nearly uniform over G = SL(2; q). This extends results by Gowers (Combinatorics, Probability & Computing, 2008) and by Babai, Nikolov, and Pyber (SODA 2008) corresponding to the independent case where A and B are product sets. We also obtain an alternative proof of their result that the product of three indepen- dent, high-entropy elements of G is nearly uniform. Unlike the previous proofs, ours does not rely on representation theory. ∗Royal Society 2010 Anniversary Research Professor. ySupported by NSF grant CCF-1319206.
    [Show full text]
  • On SZK and PP
    Electronic Colloquium on Computational Complexity, Revision 2 of Report No. 140 (2016) On SZK and PP Adam Bouland1, Lijie Chen2, Dhiraj Holden1, Justin Thaler3, and Prashant Nalini Vasudevan1 1CSAIL, Massachusetts Institute of Technology, Cambridge, MA USA 2IIIS, Tsinghua University, Beijing, China 3Georgetown University, Washington, DC USA Abstract In both query and communication complexity, we give separations between the class NISZK, con- taining those problems with non-interactive statistical zero knowledge proof systems, and the class UPP, containing those problems with randomized algorithms with unbounded error. These results significantly improve on earlier query separations of Vereschagin [Ver95] and Aaronson [Aar12] and earlier commu- nication complexity separations of Klauck [Kla11] and Razborov and Sherstov [RS10]. In addition, our results imply an oracle relative to which the class NISZK 6⊆ PP. This answers an open question of Wa- trous from 2002 [Aar]. The technical core of our result is a stronger hardness amplification theorem for approximate degree, which roughly says that composing the gapped-majority function with any function of high approximate degree yields a function with high threshold degree. Using our techniques, we also give oracles relative to which the following two separations hold: perfect zero knowledge (PZK) is not contained in its complement (coPZK), and SZK (indeed, even NISZK) is not contained in PZK (indeed, even HVPZK). Along the way, we show that HVPZK is contained in PP in a relativizing manner. We prove a number of implications of these results, which may be of independent interest outside of structural complexity. Specifically, our oracle separation implies that certain parameters of the Polariza- tion Lemma of Sahai and Vadhan [SV03] cannot be much improved in a black-box manner.
    [Show full text]
  • Adaptive Garbled RAM from Laconic Oblivious Transfer
    Adaptive Garbled RAM from Laconic Oblivious Transfer Sanjam Garg?1, Rafail Ostrovsky??2, and Akshayaram Srinivasan1 1 University of California, Berkeley fsanjamg,[email protected] 2 UCLA [email protected] Abstract. We give a construction of an adaptive garbled RAM scheme. In the adaptive setting, a client first garbles a \large" persistent database which is stored on a server. Next, the client can provide garbling of mul- tiple adaptively and adversarially chosen RAM programs that execute and modify the stored database arbitrarily. The garbled database and the garbled program should reveal nothing more than the running time and the output of the computation. Furthermore, the sizes of the garbled database and the garbled program grow only linearly in the size of the database and the running time of the executed program respectively (up to poly logarithmic factors). The security of our construction is based on the assumption that laconic oblivious transfer (Cho et al., CRYPTO 2017) exists. Previously, such adaptive garbled RAM constructions were only known using indistinguishability obfuscation or in random oracle model. As an additional application, we note that this work yields the first constant round secure computation protocol for persistent RAM pro- grams in the malicious setting from standard assumptions. Prior works did not support persistence in the malicious setting. 1 Introduction Over the years, garbling methods [Yao86,LP09,AIK04,BHR12b,App17] have been extremely influential and have engendered an enormous number of applications ? Research supported in part from DARPA/ARL SAFEWARE Award W911NF15C0210, AFOSR Award FA9550-15-1-0274, AFOSR YIP Award, DARPA and SPAWAR under contract N66001-15-C-4065, a Hellman Award and research grants by the Okawa Foundation, Visa Inc., and Center for Long-Term Cybersecurity (CLTC, UC Berkeley).
    [Show full text]
  • Resource-Competitive Algorithms1 1 Introduction
    Resource-Competitive Algorithms1 Michael A. Bender Varsha Dani Department of Computer Science Department of Computer Science Stony Brook University University of New Mexico Stony Brook, NY, USA Albuquerque, NM, USA [email protected] [email protected] Jeremy T. Fineman Seth Gilbert Department of Computer Science Department of Computer Science Georgetown University National University of Singapore Washington, DC, USA Singapore [email protected] [email protected] Mahnush Movahedi Seth Pettie Department of Computer Science Electrical Eng. and Computer Science Dept. University of New Mexico University of Michigan Albuquerque, NM, USA Ann Arbor, MI, USA [email protected] [email protected] Jared Saia Maxwell Young Department of Computer Science Computer Science and Engineering Dept. University of New Mexico Mississippi State University Albuquerque, NM, USA Starkville, MS, USA [email protected] [email protected] Abstract The point of adversarial analysis is to model the worst-case performance of an algorithm. Un- fortunately, this analysis may not always reflect performance in practice because the adversarial assumption can be overly pessimistic. In such cases, several techniques have been developed to provide a more refined understanding of how an algorithm performs e.g., competitive analysis, parameterized analysis, and the theory of approximation algorithms. Here, we describe an analogous technique called resource competitiveness, tailored for dis- tributed systems. Often there is an operational cost for adversarial behavior arising from band- width usage, computational power, energy limitations, etc. Modeling this cost provides some notion of how much disruption the adversary can inflict on the system. In parameterizing by this cost, we can design an algorithm with the following guarantee: if the adversary pays T , then the additional cost of the algorithm is some function of T .
    [Show full text]
  • FOCS 2005 Program SUNDAY October 23, 2005
    FOCS 2005 Program SUNDAY October 23, 2005 Talks in Grand Ballroom, 17th floor Session 1: 8:50am – 10:10am Chair: Eva´ Tardos 8:50 Agnostically Learning Halfspaces Adam Kalai, Adam Klivans, Yishay Mansour and Rocco Servedio 9:10 Noise stability of functions with low influences: invari- ance and optimality The 46th Annual IEEE Symposium on Elchanan Mossel, Ryan O’Donnell and Krzysztof Foundations of Computer Science Oleszkiewicz October 22-25, 2005 Omni William Penn Hotel, 9:30 Every decision tree has an influential variable Pittsburgh, PA Ryan O’Donnell, Michael Saks, Oded Schramm and Rocco Servedio Sponsored by the IEEE Computer Society Technical Committee on Mathematical Foundations of Computing 9:50 Lower Bounds for the Noisy Broadcast Problem In cooperation with ACM SIGACT Navin Goyal, Guy Kindler and Michael Saks Break 10:10am – 10:30am FOCS ’05 gratefully acknowledges financial support from Microsoft Research, Yahoo! Research, and the CMU Aladdin center Session 2: 10:30am – 12:10pm Chair: Satish Rao SATURDAY October 22, 2005 10:30 The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics Tutorials held at CMU University Center into `1 [Best paper award] Reception at Omni William Penn Hotel, Monongahela Room, Subhash Khot and Nisheeth Vishnoi 17th floor 10:50 The Closest Substring problem with small distances Tutorial 1: 1:30pm – 3:30pm Daniel Marx (McConomy Auditorium) Chair: Irit Dinur 11:10 Fitting tree metrics: Hierarchical clustering and Phy- logeny Subhash Khot Nir Ailon and Moses Charikar On the Unique Games Conjecture 11:30 Metric Embeddings with Relaxed Guarantees Break 3:30pm – 4:00pm Ittai Abraham, Yair Bartal, T-H.
    [Show full text]
  • The Limits of Post-Selection Generalization
    The Limits of Post-Selection Generalization Kobbi Nissim∗ Adam Smithy Thomas Steinke Georgetown University Boston University IBM Research – Almaden [email protected] [email protected] [email protected] Uri Stemmerz Jonathan Ullmanx Ben-Gurion University Northeastern University [email protected] [email protected] Abstract While statistics and machine learning offers numerous methods for ensuring gener- alization, these methods often fail in the presence of post selection—the common practice in which the choice of analysis depends on previous interactions with the same dataset. A recent line of work has introduced powerful, general purpose algorithms that ensure a property called post hoc generalization (Cummings et al., COLT’16), which says that no person when given the output of the algorithm should be able to find any statistic for which the data differs significantly from the population it came from. In this work we show several limitations on the power of algorithms satisfying post hoc generalization. First, we show a tight lower bound on the error of any algorithm that satisfies post hoc generalization and answers adaptively chosen statistical queries, showing a strong barrier to progress in post selection data analysis. Second, we show that post hoc generalization is not closed under composition, despite many examples of such algorithms exhibiting strong composition properties. 1 Introduction Consider a dataset X consisting of n independent samples from some unknown population P. How can we ensure that the conclusions drawn from X generalize to the population P? Despite decades of research in statistics and machine learning on methods for ensuring generalization, there is an increased recognition that many scientific findings do not generalize, with some even declaring this to be a “statistical crisis in science” [14].
    [Show full text]
  • The Computational Complexity of Nash Equilibria in Concisely Represented Games∗
    The Computational Complexity of Nash Equilibria in Concisely Represented Games¤ Grant R. Schoenebeck y Salil P. Vadhanz August 26, 2009 Abstract Games may be represented in many di®erent ways, and di®erent representations of games a®ect the complexity of problems associated with games, such as ¯nding a Nash equilibrium. The traditional method of representing a game is to explicitly list all the payo®s, but this incurs an exponential blowup as the number of agents grows. We study two models of concisely represented games: circuit games, where the payo®s are computed by a given boolean circuit, and graph games, where each agent's payo® is a function of only the strategies played by its neighbors in a given graph. For these two models, we study the complexity of four questions: determining if a given strategy is a Nash equilibrium, ¯nding a Nash equilibrium, determining if there exists a pure Nash equilibrium, and determining if there exists a Nash equilibrium in which the payo®s to a player meet some given guarantees. In many cases, we obtain tight results, showing that the problems are complete for various complexity classes. 1 Introduction In recent years, there has been a surge of interest at the interface between computer science and game theory. On one hand, game theory and its notions of equilibria provide a rich framework for modeling the behavior of sel¯sh agents in the kinds of distributed or networked environments that often arise in computer science and o®er mechanisms to achieve e±cient and desirable global outcomes in spite of the sel¯sh behavior.
    [Show full text]
  • A Polynomial-Time Approximation Algorithm for All-Terminal Network Reliability
    A Polynomial-Time Approximation Algorithm for All-Terminal Network Reliability Heng Guo School of Informatics, University of Edinburgh, Informatics Forum, Edinburgh, EH8 9AB, United Kingdom. [email protected] https://orcid.org/0000-0001-8199-5596 Mark Jerrum1 School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, United Kingdom. [email protected] https://orcid.org/0000-0003-0863-7279 Abstract We give a fully polynomial-time randomized approximation scheme (FPRAS) for the all-terminal network reliability problem, which is to determine the probability that, in a undirected graph, assuming each edge fails independently, the remaining graph is still connected. Our main contri- bution is to confirm a conjecture by Gorodezky and Pak (Random Struct. Algorithms, 2014), that the expected running time of the “cluster-popping” algorithm in bi-directed graphs is bounded by a polynomial in the size of the input. 2012 ACM Subject Classification Theory of computation → Generating random combinatorial structures Keywords and phrases Approximate counting, Network Reliability, Sampling, Markov chains Digital Object Identifier 10.4230/LIPIcs.ICALP.2018.68 Related Version Also available at https://arxiv.org/abs/1709.08561. Acknowledgements We thank Mark Huber for bringing reference [8] to our attention, Mark Walters for the coupling idea leading to Lemma 12, and Igor Pak for comments on an earlier version. We also thank the organizers of the “LMS – EPSRC Durham Symposium on Markov Processes, Mixing Times and Cutoff”, where part of the work is carried out. 1 Introduction Network reliability problems are extensively studied #P-hard problems [5] (see also [3, 22, 18, 2]).
    [Show full text]