An enumeration scheme to generate constrained exact checkerboard patterns

2008 ◽  
Vol 35 (6) ◽  
pp. 2114-2128 ◽  
Author(s):  
Horacio Hideki Yanasse ◽  
Daniel Massaru Katsurayama
Keyword(s):  
Enumeration Scheme

scholarly journals A survey on the cutting and packing problems

2020 ◽  
Vol 13 (4) ◽  
pp. 567-572
Author(s):  
Loris Faina
Keyword(s):  
Three Dimensional ◽  
Cutting And Packing ◽  
Unified Approach ◽  
Geometrical Method ◽  
Packing Problems ◽  
Enumeration Scheme

Abstract This paper presents a unified approach, based on a geometrical method (see Faina in Eur J Oper Res 114:542–556, 1999; Eur J Oper Res 126:340–354, 2000), which reduces the general two and three dimensional cutting and packing type problems to a finite enumeration scheme.

scholarly journals A new enumeration scheme for the knapsack problem

1987 ◽  
Vol 18 (2) ◽  
pp. 235-245 ◽  
Author(s):  
Horacio Hideki Yanasse ◽  
Nei Yoshihiro Soma
Keyword(s):  
Knapsack Problem ◽  
Enumeration Scheme

An implicit enumeration scheme for the batch selection problem

Networks ◽  
2004 ◽  
Vol 44 (2) ◽  
pp. 151-159 ◽  
Author(s):  
A. Agnetis ◽  
F. Rossi ◽  
S. Smriglio
Keyword(s):  
Selection Problem ◽  
Implicit Enumeration ◽  
Enumeration Scheme

An Implicit Enumeration Scheme for Proper Cut Generation

Technometrics ◽  
1970 ◽  
Vol 12 (4) ◽  
pp. 775-788 ◽  
Author(s):  
M. Bellmore ◽  
P. A. Jensen
Keyword(s):  
Implicit Enumeration ◽  
Cut Generation ◽  
Enumeration Scheme

Reorganizing topologies of Steiner trees to accelerate their eliminations

2019 ◽  
Vol 12 (01) ◽  
pp. 2050003
Author(s):  
Aymeric Grodet ◽  
Takuya Tsuchiya
Keyword(s):  
Lower Bound ◽  
Higher Dimensions ◽  
Exact Algorithms ◽  
Steiner Trees ◽  
Steiner Tree Problem ◽  
Original Algorithm ◽  
Steiner Points ◽  
Euclidean Steiner Tree Problem ◽  
Correct Topology ◽  
Enumeration Scheme

We describe a technique to reorganize topologies of Steiner trees by exchanging neighbors of adjacent Steiner points. We explain how to use the systematic way of building trees, and therefore topologies, to find the correct topology after nodes have been exchanged. Topology reorganizations can be inserted into the enumeration scheme commonly used by exact algorithms for the Euclidean Steiner tree problem in [Formula: see text]-space, providing a method of improvement different than the usual approaches. As an example, we show how topology reorganizations can be used to dynamically change the exploration of the usual branch-and-bound tree when two Steiner points collide during the optimization process. We also turn our attention to the erroneous use of a pre-optimization lower bound in the original algorithm and give an example to confirm its usage is incorrect. In order to provide numerical results on correct solutions, we use planar equilateral points to quickly compute this lower bound, even in dimensions higher than two. Finally, we describe planar twin trees, identical trees yielded by different topologies, whose generalization to higher dimensions could open a new way of building Steiner trees.

scholarly journals Method simplifying calculation of coefficients of fractional parentage for translationally invariant shell-model

Open Physics ◽  
2013 ◽  
Vol 11 (5) ◽  
Author(s):  
Saulius Mickevičius ◽  
Darius Germanas ◽  
Ramutis Kalinauskas
Keyword(s):  
Shell Model ◽  
Efficient Method ◽  
Large Scale ◽  
Particle Systems ◽  
The Other ◽  
Lower Degree ◽  
Fractional Parentage ◽  
Invariant Shell ◽  
Invariant Shell Model ◽  
Enumeration Scheme

AbstractA new procedure for large-scale calculations of the coefficients of fractional parentage (CFP) for many-particle systems is presented. The approach is based on a simple enumeration scheme for antisymmetric N particle states, and we suggest an efficient method for constructing the eigenvectors of two-particle transposition operator $$P_{N_1 ,N}$$ in a subspace where N 1 and N 2 = N − N 1 nucleons basis states are already antisymmetrized. The main result of this paper is that according to permutation operators $$P_{N_1 ,N}$$ eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.

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