eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-07-08
31:1
31:30
10.4230/LIPIcs.CCC.2021.31
article
Hardness of Constant-Round Communication Complexity
Hirahara, Shuichi
1
Ilango, Rahul
2
Loff, Bruno
3
National Institute of Informatics, Tokyo, Japan
Massachusetts Institute of Technology, Cambridge, MA, USA
INESC-Tec and University of Porto, Portugal
How difficult is it to compute the communication complexity of a two-argument total Boolean function f:[N]×[N] → {0,1}, when it is given as an N×N binary matrix? In 2009, Kushilevitz and Weinreb showed that this problem is cryptographically hard, but it is still open whether it is NP-hard.
In this work, we show that it is NP-hard to approximate the size (number of leaves) of the smallest constant-round protocol for a two-argument total Boolean function f:[N]×[N] → {0,1}, when it is given as an N×N binary matrix. Along the way to proving this, we show a new deterministic variant of the round elimination lemma, which may be of independent interest.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol200-ccc2021/LIPIcs.CCC.2021.31/LIPIcs.CCC.2021.31.pdf
NP-completeness
Communication Complexity
Round Elimination Lemma
Meta-Complexity