By Topic

Informational complexity and the direct sum problem for simultaneous message complexity

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

4 Author(s)
Chakrabarti, A. ; Dept. of Comput. Sci., Princeton Univ., NJ, USA ; Yaoyun Shi ; Wirth, A. ; Yao, A.

Given m copies of the same problem, does it take m times the amount of resources to solve these m problems? This is the direct sum problem, a fundamental question that has been studied in many computational models. We study this question in the simultaneous message (SM) model of communication introduced by A.C. Yao (1979). The equality problem for n-bit strings is well known to have SM complexity Θ(√n). We prove that solving m copies of the problem has complexity Ω(m√n); the best lower bound provable using previously known techniques is Ω(√(mn)). We also prove similar lower bounds on certain Boolean combinations of multiple copies of the equality function. These results can be generalized to a broader class of functions. We introduce a new notion of informational complexity which is related to SM complexity and has nice direct sum properties. This notion is used as a tool to prove the above results; it appears to be quite powerful and may be of independent interest.

Published in:

Foundations of Computer Science, 2001. Proceedings. 42nd IEEE Symposium on

Date of Conference:

8-11 Oct. 2001