[SCIP] SCIP - related work

[Vladimir V. Voloshinov]

Dear SCIP developers,
let me to inform you about one of our recent paper with new result in
Combinatorics Geometry

*Optimal Packings of Congruent Circles on a Square Flat Torus as
Mixed-Integer Nonlinear Optimization Problem. *
Vladimir Voloshinov and Sergey Smirnov
In: Voevodin V., Sobolev S. (eds) Supercomputing. RuSCDays 2019.
Communications in Computer and Information Science, vol 1129. Springer, Cham
DOI: https://doi.org/10.1007/978-3-030-36592-9_8

*Abstract*
Hard problems of discrete geometry may be formulated as a global
optimization problems, which may be solved by general purpose solvers
implementing branch-and-bound (B&B) algorithm. A problem of densest packing
of N equal circles in special geometrical object, so called Square Flat
Torus, ℝ^2/ℤ^2 , with the induced metric, is considered. It is formulated
as mixed-integer problem with linear and nonconvex quadratic constraints.
The open-source B&B-solver *SCIP* and its parallel implementation *ParaSCIP*
have been used to find optimal arrangements for 𝑁⩽9. The main result is a
confirmation of the conjecture on optimal packing for 𝑁=9 that was
published in 2012 by O. Musin and A. Nikitenko.

Yours,
-- 
Vladimir V. Voloshinov,
Ph.D, head of lab. C-3 "Distributed computing algorithms",
http://www.iitp.ru/ru/researchlabs/1040.htm,
Center for Distributed Computing, Institute for Information Transmission
Problems RAS, http://www.iitp.ru
web: GoogleScholar profile
<https://scholar.google.ru/citations?hl=en&user=-m4QhNEAAAAJ&view_op=list_works&sortby=pubdate>
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