2017 Fiscal Year Annual Research Report
Large scale parallelization for geometric computation and mathematical optimization
| Project/Area Number |
16H02785
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| Research Institution | Kyoto University |
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Principal Investigator |
Avis David 京都大学, 情報学研究科, 非常勤講師 (90584110)
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| Co-Investigator(Kenkyū-buntansha) |
ジョーダン チャールズハロルド 北海道大学, 情報科学研究科, 助教 (60647577)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Keywords | 幾何計算 / 大規模並列化 / 数理計画法への応用 |
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| Outline of Annual Research Achievements |
Our research plan involves 5 overlapping projects each involving myself and a subgroup of the team.I am involved in all projects.
1(Devroye)We continued our development of a theoretic basis for parallel tree search on random Galton-Watson trees. During this fiscal year we studied the value of two person games played on these trees, and the number of nodes that need to be searched in order to find the value. We are preparing a paper for publication on these results. Devroye visited me in Japan for joint research from May 22-June 3.
2(Jordan) We continued our development of mts,a generic framework for parallelizing tree search methods and applied it to reverse search algorithms. Jordan applied this framework to develop a parallel program for enumerating triangulations, in collaboration with the polymake group in Germany. We revised our mplrs paper and it has been accepted for publication in Mathematical Programming Computation.
3.(Tiwary) We revised our joint paper with Bremner and Watanabe on our algorithms-to-polytope compiler. This paper has been accepted with minor revisions by Discrete Applied Mathematics. 4(Cook,Devroye) Cook visited from May 15-June 5 to discuss parallel branch and bound. We met with Devroye for a week of research discussions on new methods of estimation for parallel branch and bound.
5(all members)Laboratory for Parallel Geometric Computation (LPGC). We continued the development and expansion of the various software packages that are distributed by our group.
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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 are proceeding along the plans we described in our proposal and have made very good progress on all 5 projects.
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| Strategy for Future Research Activity |
We will continue all 5 projects along the lines outlined in the grant application. Specific goals for the upcoming fiscal year are as follows:
1(Devroye)We will try to extend our theoretic basis for our experimental results by studying new random tree models. We will also try to model branch and bound as applied to Galton-Watson trees. I will visit Devroye and the Discrete Math and Optimization group at McGill over the summer.
2(Jordan) We will continue to develop mts to parallelize applications in reverse search, branch and bound and QBF formulae.
3.(Tiwary) We will try to find new compact extended formulations for problems in P with high extension complexity comparing them to polytopes generated by the Sparktope compiler.
4(Cook,Tiwary) We will try to extend mts to solve integer programs efficiently in parallel by adding cutting planes to QSopt. We will also study new methods of estimation for parallel tree search. Cook will visit May 22-June 3.
5(all members)Laboratory for Parallel Geometric Computation (LPGC). We will release a new version of lrslib that makes automatic use of 64-bit, 128-bit and extended precision arithmetic to greatly improve performance on combinatorial polytopes
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