[图书][B] Minimal NetworksThe Steiner Problem and Its Generalizations

AO Ivanov, AA Tuzhilin - 1994 - books.google.com
This book focuses on the classic Steiner Problem and illustrates how results of the problem's
development have generated the Theory of Minimal Networks, that is systems of" rubber" …

[图书][B] Branching solutions to one-dimensional variational problems

AO Ivanov, AA Tuzhilin - 2001 - books.google.com
This book deals with the new class of one-dimensional variational problems OCo the
problems with branching solutions. Instead of extreme curves (mappings of a segment to a …

Minimal networks: a review

AO Ivanov, AA Tuzhilin - Advances in dynamical systems and control, 2016 - Springer
Abstract Minimal Networks Theory is a branch of mathematics that goes back to 17th century
and unites ideas and methods of metric, differential, and combinatorial geometry and …

A survey of parallel and distributed algorithms for the steiner tree problem

M Bezenšek, B Robič - International Journal of Parallel Programming, 2014 - Springer
Given a set of input points, the Steiner Tree Problem (STP) is to find a minimum-length tree
that connects the input points, where it is possible to add new points to minimize the length …

A formula for the weight of a minimal filling of a finite metric space

AY Eremin - Sbornik: Mathematics, 2013 - iopscience.iop.org
We consider the problem of finding a minimal filling for a finite metric space, that is, a
weighted graph of minimal weight joining a given finite metric space. We obtain a minimax …

Current open problems in discrete and computational geometry

H Edelsbrunner, AO Ivanov, RN Karasev - Моделирование и анализ …, 2012 - mathnet.ru
We have selected problems that may not yet be well known, but have the potential to push
the research in interesting directions. In particular, we state problems that do not require …

Формула веса минимального заполнения конечного метрического пространства

АЮ Еремин - Математический сборник, 2013 - mathnet.ru
Рассматривается задача о поиске минимального заполнения конечного метрического
пространства, т. е. взвешенного графа наименьшего веса, соединяющего данное …

An analytical solution of the weighted Fermat–Torricelli problem on a unit sphere

AN Zachos - Rendiconti del Circolo Matematico di Palermo (1952-), 2015 - Springer
We obtain an analytical solution of the weighted Fermat–Torricelli (wFT) problem for a
specific equilateral geodesic triangle. This approach is a generalization of Cockayne's …

Branching geodesics in normed spaces

AO Ivanov, AA Tuzhilin - Izvestiya: Mathematics, 2002 - iopscience.iop.org
We study branching extremals of length functionals on normed spaces. This is a natural
generalization of the Steiner problem in normed spaces. We obtain criteria for a network to …

The parameterized Steiner problem and the singular Plateau problem via energy

C Mese, S Yamada - Transactions of the American Mathematical Society, 2006 - ams.org
The Steiner problem is the problem of finding the shortest network connecting a given set of
points. By the singular Plateau Problem, we will mean the problem of finding an area …