How to select constraints that help algorithms approximately solve constraint satisfaction problems

2014 Fiscal Year Final Research Report

• Project/Area Number: 24500011
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: University of Fukui
• Principal Investigator: YAMAKAMI TOMOYUKI 福井大学, 工学(系)研究科(研究院), 教授 (80230324)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 制約充足問題 / 最適化問題 / 数え上げ問題 / アルゴリズムの効率 / ＃P完全 / 対数領域計算 / プッシュダウンオートマトン / ２極値定理

Outline of Final Research Achievements

Constraint satisfaction problems (CSPs), which are problems of finding feasible solutions that satisfy given sets of constraints, appear frequently in daily life. By analyzing a close relationship between constraints and the efficiency of algorithms that solve those CSPs, I discovered the exact conditions on constraints to make solving algorithms faster, and this discovery helps me classify all counting Boolean CSPs according to their approximate computational complexity. As a direct application of a dichotomy theorem for counting CSPs, I successfully classified all counting list partition problems. Unlike rather theoretical polynomial-time computation, I examined logarithmic-space machine models and automata with pushdown stacks as memory devices, and explored a new frontier in a field of combinatorial optimization problems.

Free Research Field

計算量理論、アルゴリズム理論、最適化問題