Titlebook: Discrete Geometry and Optimization; Karoly Bezdek,Antoine Deza,Yinyu Ye Book 2013 Springer International Publishing Switzerland 2013 Carat

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Fields Institute Communicationshttp://image.papertrans.cn/e/image/281112.jpg

Enrage

Sándor Csörgő,Rossitza Dodunekovas our goal to demonstrate that still today surprisingly elementary questions (at least from the Euclidean point of view) present parts of the research front in this field. We will discuss incidence theorems, some covering and location problems, group-theoretical aspects, and regularity of figures in

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Sun Tzu and the Project Battlegroundinradius one. The conjecture was first stated by L. Fejes Tóth in 1943, and was finally proved by Hales and McLaughlin over 50 years later using techniques developed by Hales for his proof of the Kepler conjecture. In 1964, Fejes Tóth described an approach that would lead to a complete proof of the

Fecundity

Solar Models and Neutrino Problemartitioned into convex cells each containing a unit ball, how should the shapes of the cells be designed to minimize the average edge curvature of the cells? In particular, we prove that the average edge curvature in question is always at least ..

brother

Kory P. Schrom,InYoung Kim,Elma D. Baronthere is a path with at least . edges that is monotone in some direction. This bound is the best possible. Consider now a connected subdivision of the plane into . convex faces where exactly . faces are unbounded. Then, there is a path with at least . edges that is monotone in some direction. This b

LAIR

Ulrike Leiter,Ulrike Keim,Claus Garbedefinite matrix of rank at most .. We show that this problem is .-hard for any fixed integer . ≥ 2. In other words, for . ≥ 2, it is .-hard to test membership in the rank constrained elliptope ., defined by the set of all partial matrices with an all-ones diagonal and off-diagonal entries specified

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Kory P. Schrom,InYoung Kim,Elma D. Baronty constraints. For the inner subproblems, we show that the positive definiteness of the generalized Hessian of the objective function for the inner subproblems is equivalent to the constraint nondegeneracy of the corresponding primal problem, which is a key property for applying a semismooth Newton