Fixed Parameter Algorithms for DOMINATING SET and Related Problems on Planar Graphs

Abstract. We present an algorithm that constructively produces a solution to the k -DOMINATING SET problem for planar graphs in time O(c^ \sqrt k n) , where c=4^ 6\sqrt 34 . To obtain this result, we show that the treewidth of a planar graph with domination number γ (G) is O(\sqrt \rule 0pt 4pt \smash γ (G) ) , and that such a tree decomposition can be found in O(\sqrt \rule 0pt 4pt \smash γ (G) n) time. The same technique can be used to show that the k -FACE COVER problem (find a size k set of faces that cover all vertices of a given plane graph) can be solved in O(c ₁ ^ \sqrt k n) time, where c ₁ =3^ 36\sqrt 34 and k is the size of the face cover set. Similar results can be obtained in the planar case for some variants of k -DOMINATING SET, e.g., k -INDEPENDENT DOMINATING SET and k -WEIGHTED DOMINATING SET.     

限定记忆参数估计的Householder变换快速递推算法

利用Householder变换推导出一个新的最小二乘估计的限定记忆快速递推算法(RHFM).该算法具有运算量小,数值稳定性好、占用内存少的优点,可以用于各种静、动态模型的参数估计.     

An Efficient on‐Line Parameter Identification Algorithm for Nonlinear Servomechanisms with an Algebraic Technique for State Estimation

This paper presents a methodology for on‐line closed‐loop identification of a class of nonlinear servomechanisms. First, a system is defined with the same structure as the actual servomechanism, but using time‐varying estimated parameters. No coupling between the actual and the estimation systems is present. Position, velocity and acceleration errors, defined as the difference of the actual respective signals and the signals coming from the estimation system, are required in the identification method. Then, a recursive algorithm for on‐line identification of the system parameters is derived from a cost function depending on a linear combination of all the estimation errors. Velocity and acceleration estimates, required in the proposed parameter identification algorithm, are obtained by using an algebraic methodology. The identification algorithm is compared by means of real‐time experiments with an on‐line least squares algorithm with forgetting factor and an off‐line least squares algorithm with data preprocessing. Experimental results show that the proposed approach has a performance comparable to that obtained with the off‐line least squares algorithm, but with the advantage of avoiding any preprocessing.