# Computing All Restricted Skyline Probabilities on Uncertain Datasets

## TL;DR

This paper investigates the computation of restricted skyline probabilities on uncertain datasets, establishing complexity bounds and proposing efficient algorithms for practical cases with linear scoring functions, validated through extensive experiments.

## Contribution

It formalizes the problem, proves complexity bounds, and introduces new algorithms for linear scoring functions with various constraints, improving efficiency in uncertain data scenarios.

## Key findings

- No truly subquadratic algorithm exists unless the orthogonal vectors conjecture fails.
- Proposed algorithms achieve near-optimal and expected better time complexities.
- Algorithms demonstrate effectiveness and scalability through extensive experiments.

## Abstract

Restricted skyline (rskyline) query is widely used in multi-criteria decision making. It generalizes the skyline query by additionally considering a set of personalized scoring functions F. Since uncertainty is inherent in datasets for multi-criteria decision making, we study rskyline queries on uncertain datasets from both complexity and algorithm perspective. We formalize the problem of computing rskyline probabilities of all data items and show that no algorithm can solve this problem in truly subquadratic-time, unless the orthogonal vectors conjecture fails. Considering that linear scoring functions are widely used in practical applications, we propose two efficient algorithms for the case where $\calF$ is a set of linear scoring functions whose weights are described by linear constraints, one with near-optimal time complexity and the other with better expected time complexity. For special linear constraints involving a series of weight ratios, we further devise an algorithm with sublinear query time and polynomial preprocessing time. Extensive experiments demonstrate the effectiveness, efficiency, scalability, and usefulness of our proposed algorithms.