FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science
Volume 4855 of the series Lecture Notes in Computer Science pp 228-240
Communication Lower Bounds Via the Chromatic Number
- Ravi KumarAffiliated withYahoo! Research
- , D. SivakumarAffiliated withGoogle, Inc.
Abstract
We present a new method for obtaining lower bounds on communication complexity. Our method is based on associating with a binary function f a graph G f such that logχ(G f ) captures N 0(f) + N 1(f). Here χ(G) denotes the chromatic number of G, and N 0(f) and N 1(f) denote, respectively, the nondeterministic communication complexity of \(\overline{f}\) and f. Thus logχ(G f ) is a lower bound on the deterministic as well as zero-error randomized communication complexity of f. Our characterization opens the possibility of using various relaxations of the chromatic number as lower bound techniques for communication complexity. In particular, we show how various (known) lower bounds can be derived by employing the clique number, the Lovász ϑ-function, and graph entropy lower bounds on the chromatic number.
- Title
- Communication Lower Bounds Via the Chromatic Number
- Book Title
- FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science
- Book Subtitle
- 27th International Conference, New Delhi, India, December 12-14, 2007. Proceedings
- Pages
- pp 228-240
- Copyright
- 2007
- DOI
- 10.1007/978-3-540-77050-3_19
- Print ISBN
- 978-3-540-77049-7
- Online ISBN
- 978-3-540-77050-3
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- 4855
- Series ISSN
- 0302-9743
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Industry Sectors
- eBook Packages
- Editors
- Authors
-
- Ravi Kumar (1)
- D. Sivakumar (2)
- Author Affiliations
-
- 1. Yahoo! Research, USA
- 2. Google, Inc., USA
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