10152279
An on-chip IP address lookup algorithm
This paper proposes a new data compression algorithm to store the routing table in a tree structure using very little memory. This data structure is tailored to a hardware design reference model presented in this paper. By exploiting the low memory access latency and high bandwidth of on-chip memory, high-speed packet forwarding can be achieved using this data structure. With the addition of pipeline in the hardware, IP address lookup can only be limited by the memory access speed. The algorithm is also flexible for different implementation. Experimental analysis shows that, given the memory width of 144 bits, our algorithm needs only 400kb memory for storing a 20k entries IPv4 routing table and five memory accesses for a search. For a 1M entries IPv4 routing table, 9Mb memory and seven memory accesses are needed. With memory width of 1,068 bits, we estimate that we need 100Mb memory and six memory accesses for a routing table with 1M IPv6 prefixes.
12919460
Decay rate for a PH/M/2 queue with shortest queue discipline
In this paper, we consider a PH/M/2 queue in which each server has its own queue and arriving customers join the shortest queue. For this model, it has been conjectured that the decay rate of the tail probabilities for the shortest queue length in the steady state is equal to the square of the decay rate for the queue length in the corresponding PH/M/2 model with a single queue. We prove this fact in the sense that the tail probabilities are asymptotically geometric when the difference of the queue sizes and the arrival phase are fixed. Our proof is based on the matrix analytic approach pioneered by Neuts and recent results on the decay rates.
8245310
Packet classification using independent sets
This paper describes a new algorithm for packet classification using the concept of independent sets. The algorithm has very small memory requirements. The search speed is neither sensitive to the rule table nor to the percentage of wildcards in the fields. It also scales well from two dimensional classifiers to high dimensional ones. In particular, the algorithm is inherently parallel. Hardware tailored to this algorithm can achieve very fast search speed.
7249461
Equilibrium probability calculations for a discrete-time bulk queue model
Many problems in management science and telecommunications can be solved by the analysis of aDX/Dm/1 queueing model. In this paper, we use the zeros, both inside and outside the unit circle, of the denominator of the generating function of the model to obtain an explicit closed-form solution for the equilibrium probabilities of the number of customers in the system. The moments of the number of customers in the queue or in the system are also studied. When there are infinitely many zeros outside the unit circle, we propose an approximation method using polynomials. This method yields correct values for a finite number of the probabilities, the number depending on the degree of the polynomial approximation.
7393635
On a decomposition for infinite transition matrices
Heyman gives an interesting factorization of I-P, where P is the transition probability matrix for an ergodic Markov chain. We show that this factorization is valid if and only if the Markov chain is recurrent. Moreover, we provide a decomposition result which includes all ergodic, null recurrent as well as the transient Markov chains as special cases. Such a decomposition has been shown to be useful in the analysis of queues.
7415922
A numerically stable algorithm for two server queue models
In this paper, we consider a queueing system in which there are two exponential servers, each having his own queue, and arriving customers will join the shorter queue. Based on the results given in Flatto and McKean, we rewrite the formula for the probability that there are exactlyk customers in each queue, wherek = 0, 1,…. This enables us to present an algorithm for computing these probabilities and then to find the joint distribution of the queue lengths in the system. A program and numerical examples are given.
6260525
Teaching surface design made easy
All popular computer graphics textbooks have chapters on curves and surfaces [1, 5, 6, 7]. Teaching these chapters could be one of the most challenging tasks in a computer graphics course because of the involved mathematics and the difficulty of visualizing the anticipated effects of the theoretical results. We certainly can skip these chapters and only rely on the polyhedron world, because Gouraud’s or Phong’s shading algorithms could make polyhedra objects appear as realistic curvilinear ones. Unfortunately, real world applications such as ship hull and car body design are usually curvilinear and may only be approximated using polyhedron models. Thus, to address this problem and to make teaching surface design easier, we have designed a pedagogical tool as part of our NSF supported project [8]. One of our goals is to provide the students with an interactive environment which is used to visualize, experiment and verify important and fundamental concepts and algorithms. While there are good textbooks on curve and surface design [3, 4, 9], we can only find two pedagogical aids. Yen’s video program [11] only provides one way information flow. Rockwood and Chambers [10] describe a multimedia tutorial on computer aided geometric design which runs on Windows. It is basically a tutorial that introduces concepts using some animation but lacks a
38902380
Construction Algorithm of Principal Curves in the Sense of Limit
Principal curves have been defined as self-consistent, smooth, one-dimensional curves which pass through the middle of a multidimensional data set. They are nonlinear generalization of the first Principal Component. In this paper, we take a new approach by defining principal curves as continuous curves based on the local tangent space in the sense of limit. It is proved that this new principal curves not only satisfy the self-consistent property, but also are the unique existence for any given open covering. Based on the new definition, a new practical algorithm for constructing principal curves is given. And the convergence properties of this algorithm are analyzed. The new construction algorithm of principal curves is illustrated on some simulated data sets.
14642729
Flow simulation with locally-refined LBM
We simulate 3D fluid flow by a locally-refined lattice Boltzmann method (LBM) on graphics hardware. A low resolution LBM simulation running on a coarse grid models global flow behavior of the entire domain with low consumption of computational resources. For regions of interest where small visual details are desired, LBM simulations are performed on fine grids, which are separate grids superposed on the coarse one. The flow properties on boundaries of the fine grids are determined by the global simulation on the coarse grid. Thus, the locally refined fine-grid simulations follow the global fluid behavior, and model the desired small-scale and turbulent flow motion with their denser numerical discretization. A fine grid can be initiated and terminated at any time while the global simulation is running. It can also move inside the domain with a moving object to capture small-scale vortices caused by the object. Besides the performance improvement due to the adaptive simulation, the locally-refined LBM is suitable for acceleration on contemporary graphics hardware (GPU), since it involves only local and linear computations. Therefore, our approach achieves fast and adaptive 3D flow simulation for computer games and other interactive applications.
29045473
On Reduct Construction Algorithms
This paper critically analyzes reduct construction methods at two levels. At a high level, one can abstract commonalities from the existing algorithms, and classify them into three basic groups based on the underlying control structures. At a low level, by adopting different heuristics or fitness functions for attribute selection, one is able to derive most of the existing algorithms. The analysis brings new insights into the problem of reduct construction, and provides guidelines for the design of new algorithms
7425380
Enhancing DWT for Recent-Biased Dimension Reduction of Time Series Data
In many applications, old data in time series become less important as time elapses, which is a big challenge to traditional techniques for dimension reduction. To improve Discrete Wavelet Transform (DWT) for effective dimension reduction in this kind of applications, a new method, largest-latest-DWT, is designed by keeping the largest k coefficients out of the latest w coefficients at each level of DWT transform. Its efficiency and effectiveness is demonstrated by our experiments.