The Communication Complexity of Set Intersection and Multiple Equality Testing By Dawei Huang, Seth Pettie, Yixiang Zhang and Zhijun Zhang Get PDF (532 KB) In. Active 3 years, 11 months ago. Robust lower bounds for communication and stream computation. Introduction to communication complexity (TIFR: 5 Aug/Jaikumar; IMSc: 26 Aug/Prahladh) The two-party communication model (deterministic, randomized, public and private coins), Equalityâ¦ Rolim, editors. Technical Report TR11-145, Electronic Colloquium on Computational A course offered at MIT (Fall 2007). â 0 â share . 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. 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. bibtex2html 1.96. Alice and Bob each hold an n-bit string, x In. Combinatorial auctions. read-once boolean formulas. Mihai Patrascu and Erik D. Demaine. Alexander A. Sherstov. Thus P = NP n coNP [AUY]. Thus, communication complexity focuses on certain basic information theoretic aspects of computation, abstracting away messier and potentially unmanageable lower-level details. [, Mark Braverman and Anup Rao. 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. This page has been accessed at least Such a fundamental problem deserves the most thorough of studies. model. A near-optimal algorithm for estimating the entropy of a stream. Mihai Patrascu. Care has to be exercised in designating the analog of PP. Rahul Jain, Hartmut Klauck, and Shengyu Zhang. Amortized Communication Complexity of an Equality Predicate Depth-independent lower bounds on the communication complexity of We study two basic graph parameters, the chromatic number and the orthogonal rank, in the context of classical and quantum exact communication complexity. Lower bounds for predecessor searching in the cell probe model. How many bits do they need to communicate to know whether or not their strings are equal? meena() (IMSc) This completely resolves the question about the equiva- Communication Complexity Communication complexity concerns the following scenario. Troy Lee and Shengyu Zhang. How to compress interactive communication. Present a paper at the end of the course. [, Michael E. Saks and Xiaodong Sun. [. Tight bounds for the partial-sums problem. Location: A-212 (@ TIFR) and Room 327(@ IMSc) 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. Complexity classes in communication complexity theory (preliminary Randomized Communication Complexity A very natural extension of the model allows Alice and Bob to use randomization. version). We prove that the probabilistic communication complexity \"A computational introduction to number theory and algebra\", by Shoup . In. In, T. S. Jayram, Swastik Kopparty, and Prasad Raghavendra. Some version times since 1 July, 2011. http://www.tcs.tifr.res.in/~prahladh/teaching/2011-12/comm, Alexandr Andoni, T. S. Jayram, and Mihai Patrascu. complexity. Optimal space lower bounds for all frequency moments. 08/30/2019 â by Dawei Huang, et al. [, Alexander A. Sherstov. In Samson Abramsky, Cyril Gavoille, Claude Kirchner, Friedhelm Meyer Pranab Sen. Pranab Sen and Srinivasan Venkatesh. The Communication Complexity of Set Intersection and Multiple Equality Testing. Amit Chakrabarti and Ranganath Kondapally. 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]. For proving communication complexity lower bounds, we analyze the combinatorial structure imposed by protocols. The communication complexity of pointer chasing. Again the analysis of "equality" lYall, [Ra] shows that P f:. 6.895: Sketching, Streaming and Sub-linear space algorithms, In this context, we introduce the graphwise equality problem. Instructors: prahladh() & 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. complexity. Lower bounds for predecessor searching in the cell probe model. Alexander A. Sherstov. Expressing combinatorial optimization problems by linear programs. Two applications of information complexity. 2007. Course Calendar (subcribe [, Rahul Jain and Hartmut Klauck. Complexity (ECCC), 2011. In the above definition, we are concerned with the number of bits that must be deterministically transmitted between two parties. Time: Wed 11-12:30 and Fri 14-15:30 (@ TIFR) and Tue-Fri 9:30-11 (@ IMSc) Lectures. In. Arkadev Chattopadhyay and Toniann Pitassi. 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. 1.2 Our main problem Equality predicate (EQn).First of all, we remind the following classic prob-lem of communication complexity. In this context, we introduce the graphwise equality problem. Troy Lee and Adi Shraibman. (ical)) / IMSc 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¦ adshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A 31 â¢ Communication complexity â Equality checking Lower bounds for randomized read/write stream algorithms. The deterministic communication complexity of Equality is D(EQ) n. Proof. Communication Complexity of Equality comparison (Catrina and de Hoogh) Ask Question Asked 3 years, 11 months ago. Mihalis Yannakakis. Multiparty Communication Complexity2 / 36 Students taking the course for credit will be expected to: This list of references was generated using Lower bounds in communication complexity. with communication complexity is usually through the EQUALITY problem. 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. Yao, in his seminal paper answers this question by defining randomized communication complexity. The partition bound for classical communication complexity and query The space complexity of approximating the frequency moments. BPP (and, consequently, BPP ~NP). 1.3). In, Amit Chakrabarti, Graham Cormode, and Andrew McGregor. In. scribe lectures and class participation - 15%. 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. In. A separation of NP and coNP in multiparty communication Dmitry Gavinsky and Alexander A. Sherstov. Every nonzero degree-d polynomial has at most d roots. One application is to the communication complexity of Equality. 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. Communication lower bounds using dual polynomials. A course offered at Rutgers University (Spring 2010). However, one can ask the following more nuanced question. tion will refer to communication complexity classes unless TM'sare specifically mentioned. Technical Report TR11-063, Electronic Colloquium on Computational David P. Woodruff. Mihai Patrascu and Erik D. Demaine. In. Information equals amortized communication, 2011. On the communication complexity of read-once, T. S. Jayram, Ravi Kumar, and D. Sivakumar. Alice and Bob have n-bit strings, and want to figure out if they're equal while doing little communication. We study nondeterministic multiparty quantum communication with a quantum generalization of broadcasts. 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 Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. Complexity (ECCC), 2011. gap-Hamming-distance. jaikumar() (TIFR) / Boaz Barak, Mark Braverman, Xi Chen, and Anup Rao. Every nonzero degree-d polynomial has at most d roots. A very simple fact, but what is it good for? 16:198:671 Communication Complexity, 2010. Example 5 (Equality Revisited). In Noam Nisan, Tim Roughgarden, Éva Tardos, and Vijay V. Liad Blumrosen and Noam Nisan. In Leslie Ann Goldberg, Klaus Jansen, R. Ravi, and José D. P. In. In particular, we consider two types of communication problems that we call promise equality and list problems. http://www.tcs.tifr.res.in/~prahladh/teaching/2011-12/comm, TIFR In, László Babai, Peter Frankl, and Janos Simon. The same trivial upper bound holds 8f : f0;1gn f 0;1gn!f0;1g. We prove new bounds on the quantum communication complexity of the disjointness and equality problems. The one-way communication complexity of Hamming distance. Lower bounds for edit distance and product metrics via We will prove that the communication complexity of EQproblem is (n). An information statistics approach to data stream and communication We denote the class de that communication complexity could provide lower bounds for the resources used in a VLSI circuit. 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? complexity. Now, letâs give an example for the above two protocols for the equality function. (ical)), (Tentative) Course Schedule with list of potential topics. jumping. auf der Heide, and Paul G. Spirakis, editors. Suppose Alice â¦ In. 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. Piotr Indyk. De ne R(f) as smallest randomized communication complexity of â¦ 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 this paper we explore fundamental problems in randomized communication complexity such as computing Set Intersection on sets of size k and Equality â¦ A very simple fact, but what is it good for? That is, their goal is now to output f(x;y) with probability at least 0:99 (taken over the coins). 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. The answer may surprise you: just O(log n), if you allow a tiny probability of error. In My T. Thai and Sartaj Sahni, editors, Troy Lee. T. S. Jayram, Ravi Kumar, and D. Sivakumar. Course Calendar (subscribe An optimal lower bound on the communication complexity of 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. Suppose Alice and Bob have n-bit strings. Amit Chakrabarti, Graham Cormode, and Andrew McGregor. Amit Chakrabarti and Oded Regev. 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: . For both of these, it was already known that the one-round classical and one-round quantum complexities are characterized by â¦ Paul Beame, T. S. Jayram, and Atri Rudra. â Lower bound for the inner product problem â Simultaneous message passing & fingerprinting. Space lower bounds for distance approximation in the data stream â¢ Communication complexity â Equality checking â Intersection (quadratic savings) â Are exponential savings possible? One application is to the communication complexity of Equality. In. prahladh() & The multiparty communication complexity of set disjointness. We study the communication complexity of a direct sum of independent copies of the equality predicate. Everywhere-tight information cost tradeoffs for augmented index. 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. 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/) 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 There are two players with unlimited computational power, each of whom holds ann bit input, say x and y. 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). I'm familiar with the fooling set technique to obtain lower bounds for communication complexity protocols. [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. Homepage: Carsten Damm, Stasys Jukna, and Jiri Sgall. ized communication complexity such as computing Set Inter-section on sets of size kand Equality Testing between vectors of length k. Brody et al. Poincaré-type inequalities. The story of set disjointness. Vazirani, editors, Mark Braverman and Anup Rao. 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) the communication complexity problem. Unifying the landscape of cell-probe lower bounds. The communication complexity of gap Hamming distance. One of our main results is NP g; BPP. Composition theorems in communication complexity. Some bounds on multiparty communication complexity of pointer Noga Alon, Yossi Matias, and Mario Szegedy. Logarithmic lower bounds in the cell-probe model. 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 They Theorem 4. Do problem sets (approx 1 pset every month). Communication complexity under product and nonproduct distributions. Stephen Ponzio, Jaikumar Radhakrishnan, and Srinivasan Venkatesh. Towards coding for maximum errors in interactive communication. Alexander A. Sherstov.