On the enumeration of geometric objects

2014 Fiscal Year Final Research Report

• Project/Area Number: 24500008
• 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: Saitama University
• Principal Investigator: HORIYAMA Takashi 埼玉大学, 情報メディア基盤センター, 准教授 (60314530)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: アルゴリズム / 列挙アルゴリズム / 計算幾何学 / 展開図 / 多面体

Outline of Final Research Achievements

The methodology for designing enumeration algorithms of geometric objects are discussed by integrating basic technologies (e.g., BDDs (Binary Decision Diagrams), ZDDs (Zero-suppressed BDDs) and reverse search). As for the enumeration of developments of polyhedra, the efficiency of the combined method with the frontier-based ZDD construction and a removal of isomorphic developments is shown. The extension of this method is discussed for enumerating general developments (i.e., developments obtained by cutting not only the edges but also faces) of polyhedra. Moreover, the counting method for essentially different developments of any polyhedron is proposed. We can count the number of non-isomorphic developments without enumerating the developments.

Free Research Field

計算幾何学