2019 Fiscal Year Annual Research Report
TSP in Combinatorial Optimization and CSP in Theoretical Computer Science
| Project/Area Number |
18F18746
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| Research Institution | National Institute of Informatics |
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Principal Investigator |
河原林 健一 国立情報学研究所, 情報学プリンシプル研究系, 教授 (40361159)
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| Co-Investigator(Kenkyū-buntansha) |
FULLA PETER 国立情報学研究所, ビッグデータ数理国際研究センター, 外国人特別研究員
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| Project Period (FY) |
2018-11-09 – 2021-03-31
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| Keywords | graph / TSP |
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| Outline of Annual Research Achievements |
In this research project we examine known approaches to the travelling salesman problem (TSP) with the aim of analyzing the extent of their applicability to the TSP itself as well as to its variants. The goal is to develop novel and scalable algorithms for these problems with improved approximation guarantees, establish tighter lower bounds, and to deepen the theoretical understanding of the employed techniques. If time permits, we would like to implement our algorithm to run for some bench mark data.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
We extend known graphic TSP algorithms to apply for a broader class of graphs. To this end, we need to work on cut problems.
The minimum cut problem appeared as a crucial component of the complexity classification of surjective valued constraints satisfaction problems over two-element domains. Aiming to advance the classification over larger domains, we investigated various generalizations of the minimum k-way cut problem. The basic problem is known to be tractable for any fixed value of k. We found several new tractable variants of it, in particular by adding a limited number of terminals, considering the asymmetric version and nonuniform weights.
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| Strategy for Future Research Activity |
We plan to analyze the approach of Svensson et al. to the asymmetric TSP in order to identify its key components, make the algorithm self-contained by simplifying the sequence of reductions, and improve its approximation ratio. Furthermore, we aim to extend to the idea of using a solution to the dual linear program in order to establish stronger structural properties of a given instance for the symmetric or asymmetric setting.
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