Large Deviation Based Upper Bounds for the Lcs-problem
نویسندگان
چکیده
Let X := (X1, . . . ,Xn) and Y := (Y1, . . . , Yn) be two finite sequences. Let Ln designate the length of the longest sequence which occurs as a subsequence of X as well as of Y . We analyze and apply a large deviation and Montecarlo simulation based method for the computation of improved upper bounds on the Chvàtal-Sankoff constant γ, which is defined by the limit γ = limn→∞ E[Ln]/n when X and Y are random sequences with i.i.d. entries. Our theoretical results show that this method converges to the exact value of γ when a control parameter m converges to infinity. We also give upper bounds on the complexity for numerically computing γ to any given precision via this method. Our numerical experiments confirm the theory and allow us to give new upper bounds that are correct to two digits. AMS Classification: primary 05A16, 62F10; secondary 92E10.
منابع مشابه
Robust Tracking Control of Satellite Attitude Using New EKF for Large Rotational Maneuvers
Control of a class of uncertain nonlinear systems, which estimates unavailable state variables, is considered. A new approach for robust tracking control problem of satellite for large rotational maneuvers is presented in this paper. The features of this approach include a strong algorithm to estimate attitude, based on discrete extended Kalman filter combined with a continuous extended Kalman ...
متن کاملUpper bounds on the solutions to n = p+m^2
ardy and Littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. They believed that the number $mathcal{R}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{R}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1-frac{1}{p-1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is a...
متن کاملRobust Tracking Control of Satellite Attitude Using New EKF for Large Rotational Maneuvers
Control of a class of uncertain nonlinear systems, which estimates unavailable state variables, is considered. A new approach for robust tracking control problem of satellite for large rotational maneuvers is presented in this paper. The features of this approach include a strong algorithm to estimate attitude, based on discrete extended Kalman filter combined with a continuous extended Kalman ...
متن کاملA Non-linear Integer Bi-level Programming Model for Competitive Facility Location of Distribution Centers
The facility location problem is a strategic decision-making for a supply chain, which determines the profitability and sustainability of its components. This paper deals with a scenario where two supply chains, consisting of a producer, a number of distribution centers and several retailers provided with similar products, compete to maintain their market shares by opening new distribution cent...
متن کاملAn Efficient Algorithm for Reducing the Duality Gap in a Special Class of the Knapsack Problem
A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...
متن کامل