Optimization theory over large configuration spaces from the viewpoint of discrete structures

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K11670
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60010:Theory of informatics-related
• Research Institution: The University of Electro-Communications
• Principal Investigator: OKAMOTO Yoshio 電気通信大学, 大学院情報理工学研究科, 教授 (00402660)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: アルゴリズム / 計算理論 / グラフ理論 / 離散幾何学 / 量子プログラミング

Outline of Final Research Achievements

Over the four-year research period, including the extension period, 24 academic papers and 12 presentations were produced. Below are samples of the notable achievements. (1) It was demonstrated that the shortest path problem in the configuration space of graph associahedra is computationally hard. This research was accepted at ICALP, a refereed international conference on theoretical computer science with a long tradition. (2) The challenge of efficiently mapping quantum algorithms to quantum computers was shown to be computationally hard, even in highly restricted architectures. This finding was accepted at WADS, a respected refereed international conference on algorithms and data structures.

Free Research Field

離散数学

Academic Significance and Societal Importance of the Research Achievements

大規模配位空間に対して，既存研究では連結性といった位相的性質に関する研究が主に行われていたが，本研究によって，最短路やクラスタリングといった距離的性質に関する研究の成果が多く得られた．これによって，オペレーションズ・リサーチや理論物理学といった領域に大規模配位空間における最適化の数理が理論的に応用可能であることが判明した．将来的には，理論だけではなく，実用に進展することが期待される．