Document Open Access Logo

Streaming Complexity of Checking Priority Queues

Authors Nathanael Francois, Frédéric Magniez



PDF
Thumbnail PDF

File

LIPIcs.STACS.2013.454.pdf
  • Filesize: 0.66 MB
  • 12 pages

Document Identifiers

Author Details

Nathanael Francois
Frédéric Magniez

Cite AsGet BibTex

Nathanael Francois and Frédéric Magniez. Streaming Complexity of Checking Priority Queues. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 454-465, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.STACS.2013.454

Abstract

This work is in the line of designing efficient checkers for testing the reliability of some massive data structures. Given a sequential access to the insert/extract operations on such a structure, one would like to decide, a posteriori only, if it corresponds to the evolution of a reliable structure. In a context of massive data, one would like to minimize both the amount of reliable memory of the checker and the number of passes on the sequence of operations. Chu, Kannan and McGregor (M. Chu, S. Kannan, and A. McGregor, 2007) initiated the study of checking priority queues in this setting. They showed that the use of timestamps allows to check a priority queue with a single pass and memory space \tilde{\Order}(\sqrt{N}). Later, Chakrabarti, Cormode, Kondapally and McGregor (A. Chakrabarti, G. Cormode, R. Kondapally, and A. McGregor, 2010) removed the use of timestamps, and proved that more passes do not help. We show that, even in the presence of timestamps, more passes do not help, solving an open problem of (M. Chu, S. Kannan, and A. McGregor, 2007; A. Chakrabarti, G. Cormode, R. Kondapally, and A. McGregor). On the other hand, we show that a second pass, but in reverse direction shrinks the memory space to \tilde{\Order}((\log N)^2), extending a phenomenon the first time observed by Magniez, Mathieu and Nayak (F. Magniez, C. Mathieu, and A. Nayak, 2010) for checking well-parenthesized expressions.
Keywords
  • Streaming Algorithms
  • Communication Complexity
  • Priority Queue

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail