Everywhere-tight information cost tradeoffs for augmented index
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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This paper makes three main contributions to the theory of communication complexity and stream computation. First, we present new bounds on the information complexity of AUGMENTED-INDEX. In contrast to analogous results for INDEX by Jain, Radhakrishnan and Sen [J. ACM, 2009], we have to overcome the significant technical challenge that protocols for AUGMENTED-INDEX may violate the ``rectangle property'' due to the inherent input sharing. Second, we use these bounds to resolve an open problem of Magniez, Mathieu and Nayak [STOC, 2010] on the multi-pass complexity of recognizing Dyck languages. This results in a natural separation between the standard multi-pass model and the multi-pass model that permits reverse passes. Third, we present the first passive memory checkers that verify the interaction transcripts of priority queues, stacks, and double-ended queues. We obtain tight upper and lower bounds for these problems, thereby addressing an important sub-class of the memory checking framework of Blum et al. [Algorithmica, 1994].