PPT-Lower Bounds on the Communication of Distributed Graph Algo

Progress and Obstacles Rotem Oshman ADGA 2013 Overview Network Models CONGESTED CLIQUE ASYNC MESSAGEPASSING LOCAL CONGEST general network X Talk Overview Lower bound techniques CONGEST general networks reductions from 2party communication complexity. cmuedu Joshua Brody IIIS ITCS Tsinghua University Beijing China joshuaebrodygmailcom Kevin Matulef IIIS ITCS Tsinghua University Beijing China matulefgmailcom Abstract We develop a new technique for proving lower bounds in property testing by showing Our result is modular 1 We describe a carefullychosen dynamic version of set disjointness the multiphase problem and conjecture that it requires 84861 time per operation All our lower bounds follow by easy reduction 2 We reduce 3SUM to the multipha The heart of this technique is a complex ity measure for multivariate polynomials based on the linear span of their partial derivatives We use the technique to obtain new lower bounds for computing sym metric polynomials which hold over 64257elds of Indeed developing bounds on the per formance of procedures can give complementary insights By exhibiting fundamental limits of performance perhaps over restricted classes of estimators it is possible to guarantee that an a lgorithm we have developed Upper and Lower Bounds Colouring colouring of a graph is a map where with the property that whenever there is an edge with ends uv The elements of are called colours and the vertices of one colour form a colour class The chromatic number of den Xiaoming. Sun and David P. Woodruff. Chinese Academy of Sciences and IBM Research-. Almaden. Streaming Models. Long sequence of items appear one-by-one. numbers, points, edges, …. (usually) . adversarially. 2 - . Calculations. www.waldomaths.com. Copyright © . Waldomaths.com. 2010, all rights reserved. Two ropes, . A. and . B. , have lengths:. A = . 36m to the nearest metre . B = . 23m to the nearest metre.. approximate membership. dynamic data structures. Shachar. Lovett. IAS. Ely . Porat. Bar-. Ilan. University. Synergies in lower bounds, June 2011. Information theoretic lower bounds. Information theory. A combinatorial approach to P . vs. NP. Shachar. Lovett. Computation. Input. Memory. Program . Code. Program code is . constant. Input has . variable length (n). Run time, memory – grow with input length. Xiaoming. Sun and David P. Woodruff. Chinese Academy of Sciences and IBM Research-. Almaden. Streaming Models. Long sequence of items appear one-by-one. numbers, points, edges, …. (usually) . adversarially. Xiaoming. Sun and David P. Woodruff. Chinese Academy of Sciences and IBM Research-. Almaden. Streaming Models. Long sequence of items appear one-by-one. numbers, points, edges, …. (usually) . adversarially. . with Distributed Immutable View. Rong Chen. +. , . Xin. Ding. +. , . Peng. Wang. +. , Haibo Chen. +. , . Binyu . Zang. +. and Haibing Guan. *. Institute of Parallel and Distributed Systems. +. Searching. : Given a large set of distinct keys, preprocess them so searches can be performed as quickly as possible. 1. CS 840 Unit 1: Models, Lower Bounds and getting around Lower bounds. Searching. dynamic data structures. Shachar. Lovett. IAS. Ely . Porat. Bar-. Ilan. University. Synergies in lower bounds, June 2011. Information theoretic lower bounds. Information theory. is a powerful tool to prove lower bounds, e.g. in data structures.