Algebraic Complexity Theory: New Approaches and Algorithmic Applications

2019 Fiscal Year Final Research Report

• Project/Area Number: 16H05853
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Single-year Grants
• Research Field: Theory of informatics
• Research Institution: Nagoya University (2019); Kyoto University (2016-2018)
• Principal Investigator: Le Gall Francois 名古屋大学, 多元数理科学研究科, 准教授 (50584299)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 計算量理論 / アルゴリズム / 代数的問題 / 量子計算

Outline of Final Research Achievements

In this research project we developed new techniques based on algebraic complexity theory to solve problems from theoretical computer science. Our main achievements are as follows.
We first developed new approaches to solve algebraic problems, and constructed faster algorithms for rectangular matrix multiplication. We then showed how to apply in a novel way algebraic techniques to several problems from computer science. In particular, via this approach we designed fast distributed algorithms for various computational problems over networks. Finally, we designed several quantum algorithms for graph problems that are faster than the best known algorithms.

Free Research Field

理論計算機科学

Academic Significance and Societal Importance of the Research Achievements

行列積は情報処理の普遍的な計算である。本研究で開発した行列積アルゴリズムは世界最高速であり、すでに理論計算機科学に広く使われており、今後もアルゴリズムの設計の重要なツールになると期待できる。分散計算における新アプローチは、汎用性が高く、分散計算の基幹技術になる可能性が高い。開発した量子アルゴリズムも、重要なグラフ問題を解くものであり、量子計算の優位性の確立に向けて大きな役割を果たすと期待できる。