Topic
Balanced set
About: Balanced set is a research topic. Over the lifetime, 40 publications have been published within this topic receiving 491 citations.
Papers
TL;DR: A new integer programming model and a new optimal algorithm for the MCPP are presented and the simplex method is used iteratively to obtain sharp lower bounds by solving successive relaxations of this model.
Abstract: The Chinese Postman Problem is well solved when the original graph contains only arcs or only edges. The mixed Chinese Postman Problem (MCPP) is, however, NP-complete, and very few papers have been devoted to this problem. In this paper, we present a new integer programming model and a new optimal algorithm for the MCPP. The simplex method is used iteratively to obtain sharp lower bounds by solving successive relaxations of this model. Optimality is achieved by using Gomory cuts, blossom inequalities and balanced set constraints. Detailed computational results are presented. © 1996 John Wiley & Sons, Inc.
74 citations
TL;DR: This paper proposes an extrapolation scheme with the variable exponent optimized specifically for the DFT-SAPT calculations in correlation-consistent basis sets with diffuse functions and presents the scaling factors averaged over a balanced set of 10 model complexes.
Abstract: The dispersion energy term in the symmetry-adapted perturbation theory based on the density functional theory (DFT-SAPT) converges rather slowly with basis set size. Accurate results for large complexes, where only calculations in small basis sets are practical, can be obtained by extrapolation to the complete basis set limit (CBS). In this paper, we propose an extrapolation scheme with the variable exponent optimized specifically for the DFT-SAPT calculations in correlation-consistent basis sets with diffuse functions. Another way to improve the accuracy term at no additional cost is to scale the dispersion term by a fixed amount. We present the scaling factors averaged over a balanced set of 10 model complexes. The results of these schemes are compared to the high-quality DFT-SAPT/CBS interaction energies in small complexes obtained by fitting to a series of basis sets up to aug-cc-pV5Z and to the CCSD(T)/CBS interaction energies. It is shown that even the cheapest extrapolation scheme yields results that are limited by the accuracy of the DFT-SAPT approach rather than by the basis set convergence. Scaling the dispersion term allows accurate interaction energies as well as their components to be obtained using just the aug-cc-pVDZ basis set; such a calculation can be applied to complexes consisting of up to 50 first-row atoms.
73 citations
TL;DR: Caha and Koubek showed that for 6m==3, there is a balanced set P in Q"n such that 2m-e=n, but no path partition with endvertices prescribed by P exists.
45 citations
TL;DR: It is proved that forevery natural number n there exists a natural number @p"1(n) such that for every hypercube Q with dim(Q)>[email protected]"1( n) there existsA family {P"i}"i"="1^n of pairwise vertex-disjoint paths P"i between A"i and B"i for i=1,2,...,n with V(Q).
35 citations
TL;DR: In this paper, the authors established the asymptotic consistency of the balanced repeated replication variance estimators when the parameter of interest is the population quantile, and the consistency results also hold when balanced subsampling is replaced by random subsamplings.
Abstract: Inference, including variance estimation, can be made from stratified samples by selecting a balanced set of subsamples. This balanced subsampling method is generically called the balanced repeated replication method in survey data analysis, which includes McCarthy's balanced half-samples method and its extensions for more general stratified designs. We establish the asymptotic consistency of the balanced repeated replication variance estimators when the parameter of interest is the population quantile. The consistency results also hold when balanced subsampling is replaced by random subsampling. As a key technical prerequisite, we prove a Bahadur-type representation for sample quantiles in stratified random sampling.
33 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2019 | 3 |
| 2015 | 1 |
| 2012 | 3 |
| 2011 | 3 |
| 2010 | 1 |