Yaqiao Li

Joan Boyar, Shahin Kamali, Kim S. Larsen et al.

We introduce and study the weighted version of an online matching problem in the Euclidean plane with non-crossing constraints: points with non-negative weights arrive online, and an algorithm can match an arriving point to one of the unmatched previously arrived points. In the classic model, the decision on how to match (if at all) a newly arriving point is irrevocable. The goal is to maximize the total weight of matched points under the constraint that straight-line segments corresponding to the edges of the matching do not intersect. The unweighted version of the problem was introduced in the offline setting by Atallah in 1985, and this problem became a subject of study in the online setting with and without advice in several recent papers. We observe that deterministic online algorithms cannot guarantee a non-trivial competitive ratio for the weighted problem, but we give upper and lower bounds on the problem with bounded weights. In contrast to the deterministic case, we show that using randomization, a constant competitive ratio is possible for arbitrary weights. We also study other variants of the problem, including revocability and collinear points, both of which permit non-trivial online algorithms, and we give upper and lower bounds for the attainable competitive ratios. Finally, we prove an advice complexity bound for obtaining optimality, improving the best known bound.

Yi Tian Xu, Yaqiao Li, David Meger

Inspired by ideas in cognitive science, we propose a novel and general approach to solve human motion understanding via pattern completion on a learned latent representation space. Our model outperforms current state-of-the-art methods in human motion prediction across a number of tasks, with no customization. To construct a latent representation for time-series of various lengths, we propose a new and generic autoencoder based on sequence-to-sequence learning. While traditional inference strategies find a correlation between an input and an output, we use pattern completion, which views the input as a partial pattern and to predict the best corresponding complete pattern. Our results demonstrate that this approach has advantages when combined with our autoencoder in solving human motion prediction, motion generation and action classification.