Online Service with Delay

In this article, we introduce the online service with delay problem. In this problem, there are n points in a metric space that issue service requests over time, and there is a server that serves these requests. The goal is to minimize the sum of distance traveled by the server and the total delay (or a penalty function thereof) in serving the requests. This problem models the fundamental tradeoff between batching requests to improve locality and reducing delay to improve response time, which has many applications in operations management, operating systems, logistics, supply chain management, and scheduling. Our main result is to show a poly-logarithmic competitive ratio for the online service with delay problem. This result is obtained by an algorithm that we call the preemptive service algorithm . The salient feature of this algorithm is a process called preemptive service, which uses a novel combination of (recursive) time forwarding and spatial exploration on a metric space. We also generalize our results to k > 1 servers and obtain stronger results for special metrics such as uniform and star metrics that correspond to (weighted) paging problems.

Prediction the Probability of Purchases Recommended Items

This paper discusses various methods for improving recommendation systems. A comparative analysis of two models for solving classification problems is performed: random forest and CatBoostClassifier. The research was performed on the data of the purchase history of Ozon customers. Standard methods that are often used in recommendation systems were used. We implemented collaborative filtering methods, cosine similarity of products from customer views per site visit, and similarity of text data. To evaluate the results, we used special metrics that evaluate the quality of predictions of the first k objects from the recommendations: Mean average precision (map@K) and Recall at K (recall@k). When generating additional features based on various methods that reveal the similarity of objects, an increase in the quality of model forecasts is noted. The CatBoostClassifier model showed the best results.

The affine and Euclidean normalizers of the subperiodic groups

The affine and Euclidean normalizers of the subperiodic groups, the frieze groups, the rod groups and the layer groups, are derived and listed. For the layer groups, the special metrics used for plane-group Euclidean normalizers have been considered.