Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA O(n^8) X O(n^7) Linear Programming Model of the Quadratic Assignment Problem
202
0
0.0
(
0
)
Added by
Moustapha Diaby
Publication date
2014
fields
Informatics Engineering
and research's language is
English
Authors
Moustapha Diaby
Ask ChatGPT about the research
No Arabic abstract
This paper has been withdrawn because Theorem 21 and Corollary 22 are in error; The modeling idea is OK, but it needs 9-dimensional variables instead of the 8-dimensional variables defined in notations 6.9. Examples of the correct model (with 9-index variables) are: (1) Diaby, M., Linear Programming Formulation of the Set Partitioning Problem, International Journal of Operational Research 8:4 (August 2010) pp. 399-427; (2) Diaby, M., Linear Programming Formulation of the Vertex Coloring Problem, International Journal of Mathematics in Operational Research 2:3 (May 2010) pp. 259-289; (3) Diaby, M., The Traveling Salesman Problem: A Linear Programming Formulation, WSEAS Transactions on Mathematics, 6:6 (June 2007) pp. 745-754.
rate research
Read More
In this paper, we present a new linear programming (LP) formulation of the Traveling Salesman Problem (TSP). The proposed model has O(n^8) variables and O(n^7) constraints, where n is the number of cities. Our numerical experimentation shows that computational times for the proposed linear program are several orders of magnitude smaller than those for the existing model [3].
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
Three related analyses of $phi^4$ theory with $O(N)$ symmetry are presented. In the first, we review the $O(N)$ model over the $p$-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking in an ultrametric context. We demonstrate the existence of a Wilson-Fisher fixed point using an $epsilon$ expansion, and we show how to obtain leading order results for the anomalous dimensions of low dimension operators near the fixed point. Along the way, we note an important aspect of ultrametric field theories, which is a non-renormalization theorem for kinetic terms. In the second analysis, we employ large $N$ methods to establish formulas for anomalous dimensions which are valid equally for field theories over the $p$-adic numbers and field theories on $mathbb{R}^n$. Results for anomalous dimensions agree between the first and second analyses when they can be meaningfully compared. In the third analysis, we consider higher derivativ
This paper studies an asymptotic solvability problem for linear quadratic (LQ) mean field games with controlled diffusions and indefinite weights for the state and control in the costs. We employ a rescaling approach to derive a low dimensional Riccati ordinary differential equation (ODE) system, which characterizes a necessary and sufficient condition for asymptotic solvability. The rescaling technique is further used for performance estimates, establishing an $O(1/N)$-Nash equilibrium for the obtained decentralized strategies.
We determine, for the first time, the scaling dimensions of a family of fixed-charge operators stemming from the critical $O(N)$ model in 4-$epsilon$ dimensions to the leading and next to leading order terms in the charge expansion but to all-orders in the coupling. We test our results to the maximum known order in perturbation theory while determining higher order terms.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
