With the increasing popularity of firewalls, virtual private networks (VPNs) and Quality of Service (QoS) routing, packet classification becomes increasingly important in the Internet. The high-performance solutions known so far strongly rely on certain properties of the filter database to match against, such as a small number of distinct prefixes or the absence of conflicts. In this paper, we ...

A line-search method, based on retractions, is formulated on Riemannian manifolds. This Riemannian line-search method, as well as a previouslyproposed Riemannian trust-region method, are further generalized to accelerated line-search and trust-region methods, where the next iterate is allowed to be any point that produces at least as much decrease in the cost function as a fixed fraction of the...

We consider the Approximate Nearest Line Search (NLS) problem. Given a set L of N lines in the high dimensional Euclidean space R, the goal is to build a data structure that, given a query point q ∈ R, reports a line ` ∈ L such that its distance to the query is within (1+ ) factor of the distance of the closest line to the query point q. The problem is a natural generalization of the well-studi...

We consider the problem of fault-tolerant parallel search on an infinite line by n robots. Starting from the origin, the robots are required to find a target at an unknown location. The robots can move with maximum speed 1 and can communicate in wireless mode among themselves. However, among the n robots, there are f robots that exhibit byzantine faults. A faulty robot can fail to report the ta...

A BFGS method, in association with a new backtracking line search technique, is presented for solving symmetric nonlinear equations. The global and superlinear convergences of the given method are established under mild conditions. Preliminary numerical results show that the proposed method is better than the normal technique for the given problems. c © 2007 Elsevier Ltd. All rights reserved.

It is well known that the line search methods play a very important role for optimization problems. In this paper a new line search method is proposed for solving unconstrained optimization. Under weak conditions, this method possesses global convergence and R-linear convergence for nonconvex function and convex function, respectively. Moreover, the given search direction has sufficiently desce...