2002 Fiscal Year Final Research Report Summary
Analyses of Randomized Algorithms for Constraint Satisfaction Problems
| Project/Area Number |
13680400
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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 |
計算機科学
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
WATANABE Osamu Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Professor, 大学院・情報理工学研究科, 教授 (80158617)
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| Co-Investigator(Kenkyū-buntansha) |
KABASHIMA Yoshiyuki Tokyo Institute of Technology, Interdisciplinary Graduate School of Science and Engineering, Associate Professor, 大学院・総合理工学研究科, 助教授 (80260652)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Probabilistic Algorithms / Randomized Algorithm / Belief Propagation / Constraint Satisfaction Problem / Low-Density Parity Check / Average-Case Analysis of Algorism |
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| Research Abstract |
We analyzed several randomized / probablistic algorithms for various constraint satisfaction problems.
For concrete problems, we chose (1) the decoding problem for low-density parity check codes (LDPCCD), and (2) the problem of searching a satisfying assignment of simple logical formulas (SAT). For LDPCCD, we analyzed (a) a probabilistic algorithm, so called belief propagation, and (b) a randomized local search algorithm. For both algorithms, we obtained some statistical search algorithm ; based on our analysis, we could propose an improve local search algorithm.
We also obtained some (mainly two) theoretical results on the hardness of constraint satisfaction problems in general. The first one is on the hardness of problems when we know that the solution is unique ; we gave complexity theoretic characterization to the hardness. The second one is on the average-case completeness of SAT ; we showed that complenteness notions differ when changing input distribution even sligtly.
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