| 研究実績の概要 |
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 Dec 14-21,2018. 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(published and released online), in collaboration with the polymake group in Germany. We submitted our mts paper for publication. 3.(Tiwary) We revised our joint paper with Bremner and Watanabe on our algorithms-to-polytope compiler. This paper appeared on-line April 18,2019 in Discrete Applied Mathematics. 4(Cook) Cook visited from May 7-23, 2018 to discuss 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. Version 7.0 of lrslib was released October 23, 2018 which contains hybrid 64/128/gmp arithmetic. In collaboration with Ken-ichi Kawarabayashi we held an international Workshop on Graphs and Geometric Algorithms in Keihanna, Dec 17-21.
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| 今後の研究の推進方策 |
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 estimation techniques for random tree models. We will also try to model branch and bound as applied to Galton-Watson trees. Devroye will visit again this year. 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 16-25. 5(all members)Laboratory for Parallel Geometric Computation (LPGC). We will develop and release a new version of lrslib that does not require intermediate files, and a new shared memory version of lrs will be developed.
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