Showing papers by "Alejandro López-Ortiz published in 2002"

Frequency Estimation of Internet Packet Streams with Limited Space

Abstract: We consider a router on the Internet analyzing the statistical properties of a TCP/IP packet stream. A fundamental difficulty with measuring traffic behavior on the Internet is that there is simply too much data to be recorded for later analysis, on the order of gigabytes a second. As a result, network routers can collect only relatively few statistics about the data. The central problem addressed here is to use the limited memory of routers to determine essential features of the network traffic stream. A particularly difficult and representative subproblem is to determine the top k categories to which the most packets belong, for a desired value of k and for a given notion of categorization such as the destination IP address.We present an algorithm that deterministically finds (in particular) all categories having a frequency above 1/(m+1) using m counters, which we prove is best possible in the worst case. We also present a sampling-based algorithm for the case that packet categories follow an arbitrary distribution, but their order over time is permuted uniformly at random. Under this model, our algorithm identifies flows above a frequency threshold of roughly 1/?nm with high probability, where m is the number of counters and n is the number of packets observed. This guarantee is not far off from the ideal of identifying all flows (probability 1/n), and we prove that it is best possible up to a logarithmic factor. We show that the algorithm ranks the identified flows according to frequency within any desired constant factor of accuracy.

Online routing in convex subdivisions

Abstract: We consider online routing algorithms for finding paths between the vertices of plane graphs. We show (1) there exists a routing algorithm for arbitrary triangulations that has no memory and uses n...

Frequency estimation of Internet packet streams with limited space

Abstract: We consider a router on the Internet analyzing the statistical properties of a TCP/IP packet stream. A fundamental difficulty with measuring traffic behavior on the Internet is that there is simply too much data to be recorded for later analysis, on the order of gigabytes a second. As a result, network routers can collect only relatively few statistics about the data. The central problem addressed here is to use the limited memory of routers to determine essential features of the network traffic stream. A particularly difficult and representative subproblem is to determine the top k categories to which the most packets belong, for a desired value of k and for a given notion of categorization such as the destination IP address. We present an algorithm that deterministically finds (in particular) all categories having a frequency above 1/(m+1) using m counters, which we prove is best possible in the worst case. We also present a sampling-based algorithm for the case that packet categories follow an arbitrary distribution, but their order over time is permuted uniformly at random. Under this model, our algorithm identifies flows above a frequency threshold of roughly 1/√nm with high probability, where m is the number of counters and n is the number of packets observed. This guarantee is not far off from the ideal of identifying all flows (probability 1/n), and we prove that it is best possible up to a logarithmic factor. We show that the algorithm ranks the identified flows according to frequency within any desired constant factor of accuracy.

Online Parallel Heuristics and Robot Searching under the Competitive Framework

Abstract: In this paper we investigate parallel searches on m concurrent rays for a point target t located at some unknown distance along one of the rays. A group of p agents or robots moving at unit speed searches for t. The search succeeds when an agent reaches the point t. Given a strategy S the competitive ratio is the ratio of the time needed by the agents to find t using S and the time needed if the location of t had been known in advance. We provide a strategy with competitive ratio of 1 + 2(m/p - 1)(m/(m - p))m/p and prove that this is optimal. This problem has applications in multiple heuristic searches in AI as well as robot motion planning. The case p = 1is known in the literature as the cow path problem.

Robot Localization without Depth Perception

Abstract: Consider the problem of placing reflectors in a 2-D environment in such a way that a robot equipped with a basic laser can always determine its current location. The robot is allowed to swivel at its current location, using the laser to detect at what angles some reflectors are visible, but no distance information is obtained. A polygonal map of the environment and reflectors is available to the robot. We show that there is always a placement of reflectors that allows the robot to localize itself from any point in the environment, and that such a reflector placement can be computed in polynomial time on a real RAM. This result improves over previous techniques which have up to a quadratic number of ambiguous points at which the robot cannot determine its location [1, 9]. Further, we show that the problem of optimal reflector placement is equivalent to an art-gallery problem within a constant factor.

Drawing k 2 , n : A lower bound.

Abstract: We give a tradeoff theorem between the area and the aspect ratio required by any planar straight-line drawing of K2,n on the integer lattice. In particular we show that if the drawing is contained in a rectangle of area O(n) then the rectangle must have aspect ratio Ω (n), and conversely, if the aspect ratio is O(1) then the area must be Ω (n2/log2/n).