This paper proposes a simple nearest neighbor search algorithm, which provides the exact solution in terms of the Euclidean distance efficiently. Especially, we present an interesting approach to improve the speed of nearest neighbor search by proper translations of data and query although the task is inherently invariant to the Euclidean transformations. The proposed algorithm aims to eliminate nearest neighbor candidates effectively using their distance lower bounds in nonlinear embedded spaces, and further improves the lower bounds by transforming data and query through product quantized translations. Although our framework is composed of simple operations only, it achieves the state-of-the-art performance compared to existing nearest neighbor search techniques, which is illustrated quantitatively using various large-scale benchmark datasets in different sizes and dimensions.

We introduce the snowblower problem (SBP), a new optimization problem that is closely related to milling problems and to some material-handling problems. The objective in the SBP is to compute a short tour for the snowblower to follow to remove all the snow from a domain (driveway, sidewalk, etc.). When a snowblower passes over each region along the tour, it displaces snow into a nearby region. The constraint is that if the snow is piled too high, then the snowblower cannot clear the pile. We give an algorithmic study of the SBP. We show that in general, the problem is NP-complete, and we present polynomial-time approximation algorithms for removing snow under various assumptions about the operation of the snowblower. Most commercially-available snowblowers allow the user to control the direction in which the snow is thrown. We differentiate between the cases in which the snow can be thrown in any direction, in any direction except backwards, and only to the right. For all cases, we give constant-factor approximation algorithms; the constants increase as the throw direction becomes more restricted. Our results are also applicable to robotic vacuuming (or lawnmowing) with bounded capacity dust bin and to some versions of material-handling problems, in which the goal is to rearrange cartons on the floor of a warehouse.