Constant-Time Algorithms for Continuous Objects

2021 Fiscal Year Final Research Report

• Project/Area Number: 17H04676
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Single-year Grants
• Research Field: Theory of informatics
• Research Institution: National Institute of Informatics
• Principal Investigator: Yoshida Yuichi 国立情報学研究所, 情報学プリンシプル研究系, 准教授 (50636967)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 定数時間アルゴリズム / 性質検査 / 実関数 / 確率密度推定 / テンソル分解

Outline of Final Research Achievements

Constant-time algorithms are algorithms for solving a decision problem or optimization problem in constant time, independent of the input size, in an approximate manner. Although constant-time algorithms have been studied for many discrete objects, such as graphs and strings, research on constant-time algorithms for continuous objects, such as real functions, matrices and tensors over real numbers, and probability distributions in Euclidean space, has been limited. In this research project, I tackled these continuous objects and succeeded in constructing constant-time algorithms for quadratic function minimization, determining whether a real function is a linear function or a polynomial of low degree, Tucker decomposition of tensors, Gaussian process regression, and probability density estimation of nondifferentiable probability distributions.

Free Research Field

理論計算機科学

Academic Significance and Societal Importance of the Research Achievements

離散的な対象と同様に連続的な対象の場合も、入力を構造部分と擬似ランダム部分に分け、構造部分に着目することで定数時間アルゴリズムが設計できる場合があることが分かってきた。ただし離散的な対象の時のようにそれが唯一の方法であるとまでは言えていないので、引き続き研究を行っていく必要がある。またテンソル分解や確率密度推定のように実用的に使われている問題に対しても定数時間アルゴリズムが有効に活用できることがわかった。