Investing in the investigative in an age of alternative media (guest blog)

What happens to investigative journalism when traditional trade craft is disrupted by a diverse range of new platforms with different principles and practices? Polis Summer School student Rahul Radhakrishnan reports. The gritty charisma portrayed by Robert Redford and Dustin Hoffman in All The President’s Men, or Kate Beckinsale in Nothing But The Truth, or more recently, Jeff Daniels in Aaron Sorkin’s new HBO series, The Newsroom has revived the long-lost appeal and celebrity profile of the professional journalist

Partition bound is quadratically tight for product distributions

Let $f : \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ be a 2-party function. For every product distribution $\mu$ on $\{0,1\}^n \times \{0,1\}^n$, we show that $$\mathsf{CC}^\mu_{0.49}(f) = O\left(\left(\log \mathsf{prt}_{1/8}(f) \cdot \log \log \mathsf{prt}_{1/8}(f)\right)^2\right),$$ where $\mathsf{CC}^\mu_\varepsilon(f)$ is the distributional communication complexity of $f$ with error at most $\varepsilon$ under the distribution $\mu$ and $\mathsf{prt}_{1/8}(f)$ is the {\em partition bound} of $f$, as defined by Jain and Klauck [{\em Proc. 25th CCC}, 2010]. We also prove a similar bound in terms of $\mathsf{IC}_{1/8}(f)$, the {\em information complexity} of $f$, namely, $$\mathsf{CC}^\mu_{0.49}(f) = O\left(\left(\mathsf{IC}_{1/8}(f) \cdot \log \mathsf{IC}_{1/8}(f)\right)^2\right).$$ The latter bound was recently and independently established by Kol [{\em Proc. 48th STOC}, 2016] using a different technique. We show a similar result for query complexity under product distributions. Let $g : \{0,1\}^n \rightarrow \{0,1\}$ be a function. For every bit-wise product distribution $\mu$ on $\{0,1\}^n$, we show that $$\mathsf{QC}^\mu_{0.49}(g) = O\left(\left( \log \mathsf{qprt}_{1/8}(g) \cdot \log \log\mathsf{qprt}_{1/8}(g) \right)^2 \right),$$ where $\mathsf{QC}^\mu_{\varepsilon}(g)$ is the distributional query complexity of $f$ with error at most $\varepsilon$ under the distribution $\mu$ and $\mathsf{qprt}_{1/8}(g))$ is the {\em query partition bound} of the function $g$. Partition bounds were introduced (in both communication complexity and query complexity models) to provide LP-based lower bounds for randomized communication complexity and randomized query complexity. Our results demonstrate that these lower bounds are polynomially tight for {\em product} distributions.Comment: The previous version of the paper erroneously stated the main result in terms of relaxed partition number instead of partition numbe

The quantum communication complexity of the pointer chasing problem: the bit version

We consider the two-party quantum communication complexity of the bit version of the pointer chasing problem, originally studied by Klauck, Nayak, Ta-Shma and Zuckerman [KNTZ01]. We show that in any quantum protocol for this problem, the two players must exchange Δ(n/k4) qubits. This improves the previous best bound of Δ( n/22O(k)) in [KNTZ01], and comes significantly closer to the best upper bounds known O(n+k log n) (classical deterministic [PRV01]) and O(k log n+ n/k (log[k/2](n)+log k)) (classical randomized [KNTZ01]). Our proof uses a round elimination argument with correlated input generation, making better use of the information theoretic tools than in previous papers