Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition

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].

[1]  Robert Krauthgamer,et al.  The Sketching Complexity of Pattern Matching , 2004, APPROX-RANDOM.

[2]  David P. Woodruff,et al.  Lower bounds for sparse recovery , 2010, SODA '10.

[3]  Peter Bro Miltersen,et al.  On Data Structures and Asymmetric Communication Complexity , 1998, J. Comput. Syst. Sci..

[4]  Mihai Patrascu,et al.  Unifying the Landscape of Cell-Probe Lower Bounds , 2010, SIAM J. Comput..

[5]  Jaikumar Radhakrishnan,et al.  A property of quantum relative entropy with an application to privacy in quantum communication , 2009, JACM.

[6]  Farid M. Ablayev,et al.  Lower Bounds for One-Way Probabilistic Communication Complexity and Their Application to Space Complexity , 1996, Theor. Comput. Sci..

[7]  Ravi Kumar,et al.  An information statistics approach to data stream and communication complexity , 2004, J. Comput. Syst. Sci..

[8]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[9]  Manuel Blum,et al.  Checking the correctness of memories , 2005, Algorithmica.

[10]  Richard J. Lipton,et al.  Multi-party protocols , 1983, STOC.

[11]  Eyal Kushilevitz,et al.  Communication Complexity , 1997, Adv. Comput..

[12]  David P. Woodruff,et al.  On the exact space complexity of sketching and streaming small norms , 2010, SODA '10.

[13]  Moni Naor,et al.  How Efficient Can Memory Checking Be? , 2009, TCC.

[14]  David P. Woodruff,et al.  Numerical linear algebra in the streaming model , 2009, STOC '09.

[15]  Miklós Ajtai,et al.  The invasiveness of off-line memory checking , 2002, STOC '02.

[16]  Moni Naor,et al.  The complexity of online memory checking , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[17]  Claire Mathieu,et al.  Recognizing well-parenthesized expressions in the streaming model , 2009, STOC '10.

[18]  Andrew Chi-Chih Yao,et al.  Informational complexity and the direct sum problem for simultaneous message complexity , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.