ECCC-Report TR16-190https://eccc.weizmann.ac.il/report/2016/190Comments and Revisions published for TR16-190en-usMon, 28 Nov 2016 15:57:16 +0200
Paper TR16-190
| Trading information complexity for error |
Hamed Hatami,
Yuval Filmus,
Yuval Dagan,
Yaqiao Li
https://eccc.weizmann.ac.il/report/2016/190We consider the standard two-party communication model. The central problem studied in this article is how much one can save in information complexity by allowing an error of $\epsilon$.
For arbitrary functions, we obtain lower bounds and upper bounds indicating a gain that is of order $\Omega(h(\epsilon))$ and $O(h(\sqrt{\epsilon}))$. Here $h$ denotes the binary entropy function. We analyze the case of the two-bit AND function in detail to show that for this function the gain is $\Theta(h(\epsilon))$. This answers a question of [M. Braverman, A. Garg, D. Pankratov, and O. Weinstein, From information to exact communication (extended abstract), STOC'13].
We obtain sharp bounds for the set disjointness function of order $n$. For the case of the distributional error, we introduce a new protocol that achieves a gain of $\Theta(\sqrt{h(\epsilon)})$ provided that $n$ is sufficiently large. We apply these results to answer another of question of Braverman et al. regarding the randomized communication complexity of the set disjointness function.
Answering a question of [Mark Braverman, Interactive information complexity, STOC'12], we apply our analysis of the set disjointness function to establish a gap between the two different notions of the prior-free information cost. This implies that amortized randomized communication complexity is not necessarily equal to the amortized distributional communication complexity with respect to the hardest distribution.Mon, 28 Nov 2016 15:57:16 +0200https://eccc.weizmann.ac.il/report/2016/190