New Query Lower Bounds for Submodular Function Minimization

We consider submodular function minimization in the oracle model: given black-box access to a submodular set function $f:2^{[n]}\rightarrow \mathbb{R}$, find an element of $\arg\min_S \{f(S)\}$ using as few queries to $f(\cdot)$ as possible. State-of-the-art algorithms succeed with $\tilde{O}(n^2)$ queries [LeeSW15], yet the best-known lower bound has never been improved beyond $n$ [Harvey08]. We provide a query lower bound of $2n$ for submodular function minimization, a $3n/2-2$ query lower bound for the non-trivial minimizer of a symmetric submodular function, and a $\binom{n}{2}$ query lower bound for the non-trivial minimizer of an asymmetric submodular function. Our $3n/2-2$ lower bound results from a connection between SFM lower bounds and a novel concept we term the cut dimension of a graph. Interestingly, this yields a $3n/2-2$ cut-query lower bound for finding the global mincut in an undirected, weighted graph, but we also prove it cannot yield a lower bound better than $n+1$ for $s$-$t$ mincut, even in a directed, weighted graph

Air pollution from household solid fuel combustion in India: an overview of exposure and health related information to inform health research priorities

Environmental and occupational risk factors contribute to nearly 40% of the national burden of disease in India, with air pollution in the indoor and outdoor environment ranking amongst leading risk factors. It is now recognized that the health burden from air pollution exposures that primarily occur in the rural indoors, from pollutants released during the incomplete combustion of solid fuels in households, may rival or even exceed the burden attributable to urban outdoor exposures. Few environmental epidemiological efforts have been devoted to this setting, however. We provide an overview of important available information on exposures and health effects related to household solid fuel use in India, with a view to inform health research priorities for household air pollution and facilitate being able to address air pollution within an integrated rural–urban framework in the future