arXiv subjects

Yaqiao Li

Publications and source records attributed to Yaqiao Li.

22 records · Page 2Linked to original sources

arXiv2017

Information complexity of the AND function in the two-Party, and multiparty settings

In a recent breakthrough paper [M. Braverman, A. Garg, D. Pankratov, and O. Weinstein, From information to exact communication, STOC'13] Braverman et al. developed a local characterization for the zero-error information complexity in the two party model, and used it to compute the exact internal and external information complexity of the 2-bit AND function, which was then applied to determine the exact asymptotic of randomized communication complexity of the set disjointness problem. In this article, we extend their results on AND function to the multi-party number-in-hand model by proving that the generalization of their protocol has optimal internal and external information cost for certain distributions. Our proof has new components, and in particular it fixes some minor gaps in the proof of Braverman et al.

cs.CC↗

arXiv2016

Trading information complexity for error

We 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 $ε$. For arbitrary functions, we obtain lower bounds and upper bounds indicating a gain that is of order $Ω(h(ε))$ and $O(h(\sqrtε))$. 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 $Θ(h(ε))$. 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 $Θ(\sqrt{h(ε)})$ 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.

cs.CC↗

arXiv2015

A characterization of functions with vanishing averages over products of disjoint sets

Given $α_1,...,α_m \in (0,1)$, we characterize all integrable functions $f:[0,1]^m \to \mathbb{C}$ satisfying $\int_{A_1 \times ...\times A_m} f =0$ for any collection of disjoint sets $A_1,...,A_m \subseteq [0,1]$ of respective measures $α_1,...,α_m$. We use this characterization to settle some of the conjectures in [S. Janson and V. Sós, More on quasi-random graphs, subgraph counts and graph limits, arXiv:1405.6808].

math.CO↗

arXiv2013

The winning property of mixed badly approximable numbers

For any pair of real numbers $(i,j)$ with $0<i,j<1$ and $i+j=1$, we prove that the set of $p$-adic mixed $(i,j)$-badly approximable numbers $\bad_p(i, j)$ is 1/2-winning in the sense of Schmidt's game. This improves a recent result of Badziahin, Levesley, and Velani on mixed Schmidt conjecture.

math.NT↗