An Approximation Polynomial Algorithm for a Problem of Searching for the Longest Subsequence in a Finite Sequence of Points in Euclidean Space

2018 ◽  
pp. 120-130 ◽  
Author(s):  
Alexander Kel’manov ◽  
Artem Pyatkin ◽  
Sergey Khamidullin ◽  
Vladimir Khandeev ◽  
Yury V. Shamardin ◽  
...  
Keyword(s):  
Euclidean Space ◽  
Polynomial Algorithm ◽  
Finite Sequence ◽  
Longest Subsequence ◽  
Approximation Polynomial

scholarly journals Estimates of objective function minimum for solving linear fractional unconstrained combinatorial optimization problems on arrangements

2021 ◽  
pp. 32-36
Author(s):  
Tetiana Barbolina
Keyword(s):  
Combinatorial Optimization ◽  
Objective Function ◽  
Numerical Experiments ◽  
Polynomial Algorithm ◽  
Optimization Problems ◽  
Finite Sequence ◽  
Feasible Set ◽  
Combinatorial Optimization Problems ◽  
Unconstrained Problems

The paper is devoted to the study of one class of Euclidean combinatorial optimization problems — combinatorial optimization problems on the general set of arrangements with linear fractional objective function and without additional (non-combinatorial) constraints. The paper substantiates the improvement of the polynomial algorithm for solving the specified class of problems. This algorithm foresees solving a finite sequence of linear unconstrained problems of combinatorial optimization on arrangements. The modification of the algorithm is based on the use of estimates of the objective function on the feasible set. This allows to exclude some of the problems from consideration and reduce the number of problems to be solved. The numerical experiments confirm the practical efficiency of the proposed approach.

Collapsing three-dimensional convex polyhedra

1967 ◽  
Vol 63 (2) ◽  
pp. 353-357 ◽  
Author(s):  
D. R. J. Chillingworth
Keyword(s):  
Euclidean Space ◽  
Simplicial Complex ◽  
Three Dimensional ◽  
Finite Sequence ◽  
Convex Polyhedra ◽  
Free Face

If L is a subcomplex of a simplicial complex K, we say that L is obtained from K by an elementary simplical collapse if K − L consists of a simplex σ of some dimension d together with one ‘free’ face of σ, i.e. a face τ of dimension d − 1 which is a face of no other simplex of K except σ. Such a collapse is said to take place through σ from τ. If L can be obtained from K by a finite sequence of elementary simplicial collapses we say that K simplicially collapses (s-collapses) onto L, denoted by K ↘ LIf K is regarded as being embedded in some Euclidean space we shall for convenience of notation fail to distinguish between K and its underlying polyhedron.

Approximation polynomial algorithm for the data editing and data cleaning problem

2017 ◽  
Vol 27 (3) ◽  
pp. 365-370 ◽  
Author(s):  
A. A. Ageev ◽  
A. V. Kel’manov ◽  
A. V. Pyatkin ◽  
S. A. Khamidullin ◽  
V. V. Shenmaier
Keyword(s):  
Polynomial Algorithm ◽  
Data Cleaning ◽  
Data Editing ◽  
Approximation Polynomial

Symplectic capacities

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Euclidean Space ◽  
Generating Functions ◽  
Weinstein Conjecture ◽  
Finite Dimensional ◽  
Hofer Metric

This chapter returns to the problems which were formulated in Chapter 1, namely the Weinstein conjecture, the nonsqueezing theorem, and symplectic rigidity. These questions are all related to the existence and properties of symplectic capacities. The chapter begins by discussing some of the consequences which follow from the existence of capacities. In particular, it establishes symplectic rigidity and discusses the relation between capacities and the Hofer metric on the group of Hamiltonian symplectomorphisms. The chapter then introduces the Hofer–Zehnder capacity, and shows that its existence gives rise to a proof of the Weinstein conjecture for hypersurfaces of Euclidean space. The last section contains a proof that the Hofer–Zehnder capacity satisfies the required axioms. This proof translates the Hofer–Zehnder variational argument into the setting of (finite-dimensional) generating functions.

A polynomial algorithm of edge-neighbor-scattering number of trees

2016 ◽  
Vol 283 ◽  
pp. 1-5 ◽  
Author(s):  
Yong Liu ◽  
Zongtian Wei ◽  
Jiarong Shi ◽  
Anchan Mai
Keyword(s):  
Polynomial Algorithm
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