Communication Complexity (for Algorithm Designers)
نویسندگان
چکیده
منابع مشابه
Communication Complexity (for Algorithm Designers)
Preface The best algorithm designers prove both possibility and impossibility results — both upper and lower bounds. For example, every serious computer scientist knows a collection of canonical NP-complete problems and how to reduce them to other problems of interest. Communication complexity offers a clean theory that is extremely useful for proving lower bounds for lots of different fundamen...
متن کاملCS369E: Communication Complexity (for Algorithm Designers) Lecture #3: Lower Bounds for Compressive Sensing∗
We begin with an appetizer before starting the lecture proper — an example that demonstrates that randomized one-way communication protocols can sometimes exhibit surprising power. It won’t surprise you that the Equality function — with f(x,y) = 1 if and only if x = y — is a central problem in communication complexity. It’s easy to prove, by the Pigeonhole Principle, that its deterministic one-...
متن کاملCS 369 E : Communication Complexity ( for Algorithm Designers ) Lecture # 9 : Lower Bounds in Property Testing ∗
We first give a brief introduction to the field of property testing. Section 3 gives upper bounds for the canonical property of “monotonicity testing,” and Section 4 shows how to derive property testing lower bounds from communication complexity lower bounds. We won’t need to develop any new communication complexity; our existing toolbox (specifically, Disjointness) is already rich enough to de...
متن کاملCS 369 E : Communication Complexity ( for Algorithm Designers ) Lecture # 8 : Lower Bounds in Property Testing ∗
We begin in this section with a brief introduction to the field of property testing. Section 2 explains the famous example of “linearity testing.” Section 3 gives upper bounds for the canonical problem of “monotonicity testing,” and Section 4 shows how to derive property testing lower bounds from communication complexity lower bounds. These lower bounds will follow from our existing communicati...
متن کاملCS 369 E : Communication Complexity ( for Algorithm Designers ) Lecture # 6 : Data Structure Lower Bounds ∗
Next we discuss how to use communication complexity to prove lower bounds on the performance — meaning space, query time, and approximation — of data structures. Our case study will be the high-dimensional approximate nearest neighbor problem. There is a large literature on data structure lower bounds. There are several different ways to use communication complexity to prove such lower bounds, ...
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ژورنال
عنوان ژورنال: Foundations and Trends® in Theoretical Computer Science
سال: 2016
ISSN: 1551-305X,1551-3068
DOI: 10.1561/0400000076