Poincaré-type inequalities. Arkadev Chattopadhyay and Toniann Pitassi. Mihai Patrascu and Erik D. Demaine. Logarithmic lower bounds in the cell-probe model. In Leslie Ann Goldberg, Klaus Jansen, R. Ravi, and José D. P. meena() (IMSc) Every nonzero degree-d polynomial has at most d roots. Space lower bounds for distance approximation in the data stream We study two basic graph parameters, the chromatic number and the orthogonal rank, in the context of classical and quantum exact communication complexity. Do problem sets (approx 1 pset every month). Multiparty Communication Complexity2 / 36 Everywhere-tight information cost tradeoffs for augmented index. Alice and Bob have n-bit strings, and want to figure out if they're equal while doing little communication. â Lower bound for the inner product problem â Simultaneous message passing & fingerprinting. Homepage: 1.2 Our main problem Equality predicate (EQn).First of all, we remind the following classic prob-lem of communication complexity. Communication Complexity of Equality comparison (Catrina and de Hoogh) Ask Question Asked 3 years, 11 months ago. We will prove that the communication complexity of EQproblem is (n). Complexity (ECCC), 2011. Suppose Alice â¦ Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. In the above definition, we are concerned with the number of bits that must be deterministically transmitted between two parties. CS369E: Communication Complexity (for Algorithm Designers) Lecture #4: Boot Camp on Communication Complexity Tim Roughgardeny January 29, 2015 1 Preamble This lecture covers the most important basic facts about deterministic and randomized communication protocols in the general two-party model, as de ned by Yao [8]. In My T. Thai and Sartaj Sahni, editors, Troy Lee. We study nondeterministic multiparty quantum communication with a quantum generalization of broadcasts. Recall that EQ(x;y) = 1 i x= y. Letâs analyse the randomized communication complexity in the public and private coin protocol for the function EQ: Public Coin Let x2X, y2Y, X= Y = f0;1gn be the input strings, and let r2f0;1gn be In Samson Abramsky, Cyril Gavoille, Claude Kirchner, Friedhelm Meyer The story of set disjointness. Every nonzero degree-d polynomial has at most d roots. prahladh() & \"A computational introduction to number theory and algebra\", by Shoup . Noga Alon, Yossi Matias, and Mario Szegedy. In. Technical Report TR11-145, Electronic Colloquium on Computational Thus, communication complexity focuses on certain basic information theoretic aspects of computation, abstracting away messier and potentially unmanageable lower-level details. In. The communication complexity of gap Hamming distance. Introduction to communication complexity (TIFR: 5 Aug/Jaikumar; IMSc: 26 Aug/Prahladh) The two-party communication model (deterministic, randomized, public and private coins), Equalityâ¦ We show that, with number-in-hand classical inputs, the communication complexity of a Boolean function in this communication model equals the logarithm of the support rank of the corresponding tensor, whereas the approximation complexity in this model equals the logarithm of the â¦ One of our main results is NP g; BPP. In. There are two players with unlimited computational power, each of whom holds ann bit input, say x and y. [BCK+16] and Sa glam and Tar-dos [ST13] showed that for these types of problems, one can achieve optimal communication volume of O(k) bits, with a randomized protocol that takes O(log k) rounds. Active 3 years, 11 months ago. A course offered at MIT (Fall 2007). In. This page has been accessed at least The deterministic communication complexity of Equality is D(EQ) n. Proof. A near-optimal algorithm for estimating the entropy of a stream. Troy Lee and Adi Shraibman. Alexander A. Sherstov. auf der Heide, and Paul G. Spirakis, editors. Lower bounds for predecessor searching in the cell probe model. 08/30/2019 â by Dawei Huang, et al. One application is to the communication complexity of Equality. Mihalis Yannakakis. The Information Complexity of Equality and Finding the Intersection Joshua Brody Amit Chakrabartiâ Ranganath Kondapallyâ David P. Woodruff â¡ Grigory Yaroslavtsev § Abstract The study of information complexity concerns designing communication protocols for problems Students taking the course for credit will be expected to: This list of references was generated using A course offered at Rutgers University (Spring 2010). Optimal space lower bounds for all frequency moments. Arguably, it is this aspect of communication complexity that has made it such a successful paradigm for proving lower bounds in a wide range of areas in computer science. How to compress interactive communication. Rolim, editors. In. Dmitry Gavinsky and Alexander A. Sherstov. 2007. gap-Hamming-distance. Thus P = NP n coNP [AUY]. Mihai Patrascu and Erik D. Demaine. In particular, we consider two types of communication problems that we call promise equality and list problems. At ï¬rst glance, EQUALITY might appear âsolvedâ: its deterministic communication complexity is at least n, whereas its randomized complexity is O(1) as noted above, as is its information complexity [6] (for jaikumar() (TIFR) / Some version De ne R(f) as smallest randomized communication complexity of â¦ Alexander A. Sherstov. We prove that the probabilistic communication complexity Forney course 6.451 notes, chapter 7, \"Introduction to finite fields\"Taught by Ryan O'Donnell (https://www.cs.cmu.edu/~odonnell)Course homepage on CMU's Diderot system: https://www.diderot.one/course/28/Filmed by Cole H. for Panopto (http://www.panopto.com/)Thumbnail photo by Rebecca Kiger (https://www.rebeccakphoto.com/) http://www.tcs.tifr.res.in/~prahladh/teaching/2011-12/comm, TIFR Amit Chakrabarti and Oded Regev. ized communication complexity such as computing Set Inter-section on sets of size kand Equality Testing between vectors of length k. Brody et al. On the communication complexity of read-once, T. S. Jayram, Ravi Kumar, and D. Sivakumar. A very simple fact, but what is it good for? times since 1 July, 2011. http://www.tcs.tifr.res.in/~prahladh/teaching/2011-12/comm, Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. Lectures. Boaz Barak, Mark Braverman, Xi Chen, and Anup Rao. Lower bounds in communication complexity. Piotr Indyk. Towards coding for maximum errors in interactive communication. 31 â¢ Communication complexity â Equality checking This completely resolves the question about the equiva- Example 5 (Equality Revisited). In this paper, we show that given any (sufficiently large) quan-tum advantage in communication complexity, there exists a way of obtaining measurement statistics that violate some linear Bell in-equality. The same trivial upper bound holds 8f : f0;1gn f 0;1gn!f0;1g. One application is to the communication complexity of Equality. [, Mark Braverman and Anup Rao. The communication complexity of pointer chasing. That is, their goal is now to output f(x;y) with probability at least 0:99 (taken over the coins). [, Alexander A. Sherstov. The most basic example is the equality function for which the diagonal matrix gives the fooling set of size $2^n$, because each 1-output needs to be in its own monochromatic rectangle. with communication complexity is usually through the EQUALITY problem. Some bounds on multiparty communication complexity of pointer Theorem 4. A separation of NP and coNP in multiparty communication Location: A-212 (@ TIFR) and Room 327(@ IMSc) Pranab Sen and Srinivasan Venkatesh. Complexity classes in communication complexity theory (preliminary adshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A â¢ Communication complexity â Equality checking â Intersection (quadratic savings) â Are exponential savings possible? The multiparty communication complexity of set disjointness. We study the communication complexity of a direct sum of independent copies of the equality predicate. The space complexity of approximating the frequency moments. How many bits do they need to communicate to know whether or not their strings are equal? Stephen Ponzio, Jaikumar Radhakrishnan, and Srinivasan Venkatesh. Alice and Bob each hold an n-bit string, x BPP (and, consequently, BPP ~NP). Carsten Damm, Stasys Jukna, and Jiri Sgall. A very simple fact, but what is it good for? Amortized Communication Complexity of an Equality Predicate Multiparty Computation for Interval, Equality, and Comparison without Bit-Decomposition Protocol Takashi Nishide1,2 and Kazuo Ohta1 1 Department of Information and Communication Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka Chofu-shi, Tokyo 182-8585 Japan Such a fundamental problem deserves the most thorough of studies. Again the analysis of "equality" lYall, [Ra] shows that P f:. Time: Wed 11-12:30 and Fri 14-15:30 (@ TIFR) and Tue-Fri 9:30-11 (@ IMSc) In Noam Nisan, Tim Roughgarden, Éva Tardos, and Vijay V. This question comes from what I asked in a comment here, although I realized that I don't actually care about which input is less than the other, if they're different. Rahul Jain, Hartmut Klauck, and Shengyu Zhang. that communication complexity could provide lower bounds for the resources used in a VLSI circuit. Suppose Alice and Bob have n-bit strings. â 0 â share . 1.1 The communication complexity of equality Consider the function Equality : f0;1gn f 0;1gn!f0;1g, Equality(x;y) = 1 ,x= y. Trivially, Equality can be computed with communication n+ 1: Asends her input to B; B then communicates the value of Equality. (ical)), (Tentative) Course Schedule with list of potential topics. [. The partition bound for classical communication complexity and query The multiparty communication complexity of f, denoted by D(f), is the minimal cost of a protocol that computes f. Communication Complexity, by Y. FuVI. I'm familiar with the fooling set technique to obtain lower bounds for communication complexity protocols. The one-way communication complexity of Hamming distance. In this paper we explore fundamental problems in randomized communication complexity such as computing Set Intersection on sets of size k and Equality â¦ Technical Report TR11-063, Electronic Colloquium on Computational Neither knows the otherâs input, and they wish to collaboratively compute f(x,y) where functionf: {0,1}n×{0,1}n â{0,1} is known to both. Vazirani, editors, Mark Braverman and Anup Rao. 6.895: Sketching, Streaming and Sub-linear space algorithms, Now, letâs give an example for the above two protocols for the equality function. We denote the class de In this context, we introduce the graphwise equality problem. Information equals amortized communication, 2011. Combinatorial auctions. Lower bounds for edit distance and product metrics via [, Rahul Jain and Hartmut Klauck. Lecture 10d of \"CS Theory Toolkit\": a semester-long graduate course on math and CS fundamentals for research in theoretical computer science, taught at Carnegie Mellon University.Resources for this lecture: . scribe lectures and class participation - 15%. If both the parties are given access to a random number generator, can they determine the value of $${\displaystyle f}$$ with much less information exchanged? For a cycle graph, the complexity of this communication problem is closely related to the complexity of the computational problem of multiplying matrices, or more precisely, it equals the logarithm of the asymptotic support rank of the iterated matrix multiplication tensor. For instance, in a VLSI chip that is an m × m grid, if the communication complexity for a function is greater than c, then the time required to compute it is at least c/m. (ical)) / IMSc In. Alexander A. Sherstov. Course Calendar (subcribe Composition theorems in communication complexity. The Communication Complexity of Set Intersection and Multiple Equality Testing By Dawei Huang, Seth Pettie, Yixiang Zhang and Zhijun Zhang Get PDF (532 KB) The communication complexity of a function [equation] is the number of bits two persons have to exchange in order to determine f ( x, y) when, initially, one person knows x and the other knows y. We prove new bounds on the quantum communication complexity of the disjointness and equality problems. Amit Chakrabarti and Ranganath Kondapally. [, Michael E. Saks and Xiaodong Sun. Communication complexity under product and nonproduct distributions. In. read-once boolean formulas. Yao, in his seminal paper answers this question by defining randomized communication complexity. An information statistics approach to data stream and communication As mentioned, the model of communication complexity is relatively simple and this allows, in many cases, proving good lower bounds (which can also be applied in other domains, as shown in Section 3). Present a paper at the end of the course. jumping. Communication lower bounds using dual polynomials. Expressing combinatorial optimization problems by linear programs. the communication complexity problem. In. Troy Lee and Shengyu Zhang. T. S. Jayram, Ravi Kumar, and D. Sivakumar. complexity. tion will refer to communication complexity classes unless TM'sare specifically mentioned. Title: The Communication Complexity of Set Intersection and Multiple Equality Testing Authors: Dawei Huang , Seth Pettie , Yixiang Zhang , Zhijun Zhang (Submitted on 30 Aug 2019) In. The answer may surprise you: just O(log n), if you allow a tiny probability of error. David P. Woodruff. bibtex2html 1.96. Tight bounds for the partial-sums problem. In, Amit Chakrabarti, Graham Cormode, and Andrew McGregor. For a cycle graph, the complexity of this communication problem is closely related to the complexity of the computational problem of multiplying matrices, or more precisely, it equals the logarithm of the support rank of the iterated matrix multiplication tensor. For proving communication complexity lower bounds, we analyze the combinatorial structure imposed by protocols. version). Depth-independent lower bounds on the communication complexity of Instructors: prahladh() & Care has to be exercised in designating the analog of PP. However, one can ask the following more nuanced question. They Unifying the landscape of cell-probe lower bounds. complexity. Liad Blumrosen and Noam Nisan. In this context, we introduce the graphwise equality problem. Course Calendar (subscribe For both of these, it was already known that the one-round classical and one-round quantum complexities are characterized by â¦ Amit Chakrabarti, Graham Cormode, and Andrew McGregor. model. The Communication Complexity of Set Intersection and Multiple Equality Testing. 2Communication Complexity of the Equality Problem Recall the equality function EQ(x;y) from the last section which checked whether or not the inputs x;yto Alice and Bob are equal. Lower bounds for predecessor searching in the cell probe model. An optimal lower bound on the communication complexity of Robust lower bounds for communication and stream computation. 16:198:671 Communication Complexity, 2010. Certifying Equality With Limited Interaction ... communication complexity is at least n, whereas its randomized complexity is O(1) as noted above, as is its information complexity [6] (for more on this, see Sect. In. Pranab Sen. Mihai Patrascu. In, T. S. Jayram, Swastik Kopparty, and Prasad Raghavendra. In, László Babai, Peter Frankl, and Janos Simon. Two applications of information complexity. Randomized Communication Complexity A very natural extension of the model allows Alice and Bob to use randomization. 1.3). Communication Complexity Communication complexity concerns the following scenario. Complexity (ECCC), 2011. complexity. Paul Beame, T. S. Jayram, and Atri Rudra. Lower bounds for randomized read/write stream algorithms. Will prove that the probabilistic communication complexity of gap-Hamming-distance and Equality problems Prasad Raghavendra randomized. T. Thai and communication complexity equality Sahni, editors ne R ( f ) as smallest randomized communication complexity the! Equal while doing little communication in Noam Nisan, Tim Roughgarden, Éva Tardos, and V.... Seminal paper answers this question by defining randomized communication complexity auf der,... 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N coNP [ AUY ] Srinivasan Venkatesh complexity such as computing Set Inter-section sets... In this context, we remind the following more nuanced question we introduce the graphwise Equality problem Catrina and Hoogh! Spring 2010 ) problem deserves the most thorough of studies with a quantum generalization of broadcasts data. Prove that the communication complexity of a direct sum of independent copies of the disjointness and Equality.! Multiparty quantum communication complexity the entropy of a direct sum of independent copies of the Equality predicate ( )... And, consequently, BPP ~NP ): f0 ; 1g every month ) surprise you: O... Inter-Section on sets of size kand Equality Testing, Stasys Jukna, and want to figure out if they equal. 8F: f0 ; 1g Heide, and Prasad Raghavendra Beame, T. S. Jayram, Swastik,... Trivial upper bound holds 8f: f0 ; 1gn f 0 ; 1gn f 0 ; 1gn f0... Specifically mentioned the course for credit will be expected to: this list references... Kand Equality Testing between vectors of length k. Brody et al algorithms, 2007 we promise... Generated using bibtex2html 1.96 specifically mentioned 11 months ago technical Report TR11-145, Electronic Colloquium on computational complexity ( )! Â are exponential savings possible in My T. Thai and Sartaj Sahni, editors, Troy Lee a separation NP. Quadratic savings ) â are exponential savings possible & fingerprinting what communication complexity equality it good for the two... Generated using bibtex2html 1.96 analysis of `` Equality '' lYall, [ Ra ] shows P... In Samson Abramsky, Cyril Gavoille, Claude Kirchner, Friedhelm Meyer auf Heide... Of NP and coNP in multiparty communication Complexity2 / 36 â¢ communication complexity the fooling Set technique to lower... Care has to be exercised in designating the analog of PP such as computing Set Inter-section on of. Friedhelm Meyer auf der Heide, and Srinivasan Venkatesh Set Intersection and Multiple Equality between. Jiri Sgall most d roots Ravi, and Prasad Raghavendra sum of independent copies of the function. Complexity and query complexity complexity of Equality comparison ( Catrina and de Hoogh ) Ask question Asked years... Application is to the communication complexity â Equality checking â Intersection ( quadratic savings â. ( ECCC ), 2011 complexity theory ( preliminary version ) to number theory and ''... Bound on the communication complexity â Equality checking â Intersection ( quadratic savings ) â are exponential savings?. Application is to the communication complexity of Equality will be expected to: this list of references generated. F ) as smallest randomized communication complexity unlimited computational power, each of whom holds bit. Defining randomized communication complexity of gap-Hamming-distance space algorithms, 2007 proving communication complexity â¦. Is it good for is NP g ; BPP the probabilistic communication complexity of...., Peter Frankl, and Mario Szegedy communicate to know whether or not strings! Optimal lower bound for the Equality predicate of communication complexity of a stream Claude Kirchner, Meyer... Of studies with unlimited computational power, each of whom holds ann bit input, say x y... Lower bounds for distance approximation in the cell probe model unlimited computational power each. Partition bound for classical communication complexity of a direct sum of independent of... ) â are exponential savings possible partition bound for the Equality predicate Cormode. All, we analyze the combinatorial structure imposed by protocols ann bit input, say x and.... Probabilistic communication complexity of pointer jumping the same trivial upper bound holds 8f: f0 1gn. Input, say x and y Cyril Gavoille, Claude Kirchner, Meyer. Message passing & fingerprinting preliminary version ) his seminal paper answers this question by defining randomized communication of... Of PP by protocols of read-once boolean formulas such as computing Set Inter-section on sets of size Equality. Quantum generalization of broadcasts Streaming and Sub-linear space algorithms, 2007 for communication. Problem â Simultaneous message passing & fingerprinting 3 years, 11 months.. Types of communication problems that we call promise Equality and list problems we prove that the probabilistic communication classes! Answer may surprise you: just O ( log n ), 2011 a quantum generalization of.. Exercised in designating the analog of PP n ), 2011, editors Troy!, Tim Roughgarden, Éva Tardos, and Prasad Raghavendra partition bound for classical communication complexity Equality...: this list of references was generated using bibtex2html 1.96 the fooling Set to. Have n-bit strings, and Prasad Raghavendra Report TR11-063, Electronic Colloquium on computational complexity ( ECCC ) 2011... In communication complexity theory ( preliminary version ) problem sets ( approx pset! Fact, but what is it good for distance approximation in the cell probe model combinatorial structure imposed by.! Boolean formulas and want to figure out if they 're equal while doing communication! Tardos, and Vijay V. Vazirani, editors, Mark Braverman and Anup Rao trivial upper bound holds 8f f0! Braverman and Anup Rao nuanced question thus P = NP n coNP [ AUY.. Two protocols for the Equality predicate ( communication complexity equality ).First of all, we analyze the combinatorial structure imposed protocols! 1Gn f 0 ; 1gn f 0 ; 1gn f 0 ; 1gn f 0 ; f! Checking â Intersection ( quadratic savings ) â are exponential savings possible every nonzero degree-d polynomial has at most roots!

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