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Communication Complexity and When Dubious Data Structures can be Detected

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Communication complexity is one of the most general and useful techniques for proving lower bounds in theoretical computer science. For example, it has been used to prove lower bounds in data structures, circuits, pseudorandomness, data streaming, and property testing. Communication problems capture the innate hardness of many problems and therefore their lower bounds can be leveraged to prove lower bounds on a variety of applications. In this talk, I will present the problem of detecting dubious data structures and show lower bounds for it using communication complexity.

Suppose we have access to an untrusted implementation of a data structure, hosted Somewhere In The Cloud. We engage this data structure in a (very) long session of operations, resulting in an interaction stream. Can we decide whether the data structure worked correctly, using much less space than it would take to reimplement its functionality? This question is one of a large and growing class of questions on Data Stream Algorithms, i.e., algorithms that get to access their input only in streaming—-rather than random-access—-fashion, and must use space sublinear in the input size. We shall see that the answer to our particular question is “Yes”, for several natural data structures, including priority queues, stacks, queues and dequeues.

I will present the outline of our algorithm that uses O(sqrt(n)) space in the worst case and also prove that this space bound is tight using a novel information theoretic lower bound for a communication game called Augmented Index.

(Joint work with Chakrabarti, Cormode, and McGregor)

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