2007 Fiscal Year Final Research Report Summary
On Computational Complexity of Computing Jones Polynomials
| Project/Area Number |
17500014
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Nihon University |
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Principal Investigator |
TANI Seiichi Nihon University, College of Humanities and Sciences, Professor (70266708)
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| Co-Investigator(Kenkyū-buntansha) |
YAKU Takeo Nihon University, College of Humanities and Sciences, Professor (90102821)
TODA Seinosuke Nihon University, College of Humanities and Sciences, Professor (90172163)
HARA Masao Tokai University, Department of Mathematical Science, Associate Professor (10238165)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Computational topoloay / Jones polynomial / discrete al aorithm / computational complexity / knot theory |
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| Research Abstract |
Knot theory is a subfield of topology. A knot is a simple (non-self-intersecting) closed curve embedded in R^3. More generally, one may study links. A link is a finite collection of disjointly embedded knots. Works on knot theory have led to many important advances in other areas, biology, chemistry and physics. For classifying and characterizing links, various invariants have been defined and profoundly studied in knot theory. The Jones polynomial is a useful invariant. It is known that computing the Jones polynomial is generally #P-hard. It is expected to require exponential time in the worst case. Recently, it has been recognized that it is important to compute Jones polynomials for links with reasonable restrictions.
EIn this project, we showed that Jones polynomials of pretzel links are computable in O(n^2) time, where n is the number of the edges in the input Tait graph. Moreover, we propose a fast algorithm for computing Jones polynomials of Montesinos links. Given the Tait graph of a Montesinos diagram with n edges, our algorithm runs with O(n) additions and multiplications in polynomials of degree O(n), namely in O(n^2log {n}) time.
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Research Products
(26 results)
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[Presentation] Temporal Reasoning System for the Digital Theater Library2007
Author(s)
S., Yoshioka, S., Tani, S., Toda, M., Morii, K., Kohno
Organizer
11th of the TASTED Conference on Internet and Multimedia Systems and Applications
Place of Presentation
Honolulu, Hawaii, USA
Year and Date
2007-08-11
Description
「研究成果報告書概要(欧文)」より
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[Presentation] 演劇資料アーカイブに対する年代推論システム2006
Author(s)
吉岡 卓, 森井 マスミ, 谷 聖一, 紅野 謙介, 戸田 誠之助
Organizer
人文科学とコンピュータシンポジウムじんもんこん2006
Place of Presentation
同志社大学
Year and Date
2006-12-14
Description
「研究成果報告書概要(和文)」より
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