Mordecai J. Golin

Bio: Mordecai J. Golin is an academic researcher from Hong Kong University of Science and Technology. The author has contributed to research in topics: Huffman coding & Time complexity. The author has an hindex of 24, co-authored 162 publications receiving 2498 citations. Previous affiliations of Mordecai J. Golin include Max Planck Society & University of Science and Technology.

On the optimal placement of web proxies in the Internet

Abstract: Web caching or web proxy has been considered as the prime vehicle of coping with the ever-increasing demand for information retrieval over the Internet, the WWW being a typical example. Existing work on web proxy has primarily focused on content based caching; relatively less attention has been given to the development of proper placement strategies for the potential web proxies in the Internet. In this paper, we argue that the placement of web proxies is critical to the performance and further investigates the optimal placement policy of web proxies for a target web server in the Internet. The objective is to optimize a given performance measure for the target web server subject to system resources and traffic pattern. Specifically, we are interested in finding the optimal placement of multiple web proxies (M) among potential sites (N) under a given traffic pattern. We show this can be modeled a dynamic programming problem. We further obtain the optimal solution for the tree topology using O(N/sup 3/M/sup 2/) time.

A dynamic programming algorithm for constructing optimal prefix-free codes with unequal letter costs

Abstract: We consider the problem of constructing prefix-free codes of minimum cost when the encoding alphabet contains letters of unequal length. The complexity of this problem has been unclear for thirty years with the only algorithm known for its solution involving a transformation to integer linear programming. We introduce a new dynamic programming solution to the problem. It optimally encodes n words in O(n/sup C+2/) time, if the costs of the letters are integers between 1 and C. While still leaving open the question of whether the general problem is solvable in polynomial time, our algorithm seems to be the first one that runs in polynomial time for fixed letter costs.

On the Optimal Placement of Web Proxies in the Internet: The Linear Topology

Abstract: Web caching or web proxy has been considered as the prime vehicle to cope with the ever-increasing demand for information retrieval over the Internet, WWW being a typical example. The existing work on web proxy has primarily focused on content based caching; relatively less attention has been given to the development of proper placement strategies for the potential web proxies in the Internet. This paper investigates the optimal placement policy of web proxies for a target web server in the Internet. The objective is to minimize the overall latency of searching the target web server subject to the network resources and traffic pattern. Specifically, we are interested in finding the optimal placement of multiple web proxies (m) among the potential sites (n) under a given traffic pattern. We model the problem as a Dynamic Programming problem, and we obtain an optimal solution for a linear array topology using O(n 2 m) time.

An optimal algorithm for approximate nearest neighbor searching fixed dimensions

Abstract: Consider a set of S of n data points in real d-dimensional space, Rd, where distances are measured using any Minkowski metric. In nearest neighbor searching, we preprocess S into a data structure, so that given any query point q∈ Rd, is the closest point of S to q can be reported quickly. Given any positive real ϵ, data point p is a (1 +ϵ)-approximate nearest neighbor of q if its distance from q is within a factor of (1 + ϵ) of the distance to the true nearest neighbor. We show that it is possible to preprocess a set of n points in Rd in O(dn log n) time and O(dn) space, so that given a query point q ∈ Rd, and ϵ > 0, a (1 + ϵ)-approximate nearest neighbor of q can be computed in O(cd, ϵ log n) time, where cd,ϵ≤d ⌈1 + 6d/ϵ⌉d is a factor depending only on dimension and ϵ. In general, we show that given an integer k ≥ 1, (1 + ϵ)-approximations to the k nearest neighbors of q can be computed in additional O(kd log n) time.

Efficient Belief Propagation for Early Vision

Abstract: Markov random field models provide a robust and unified framework for early vision problems such as stereo and image restoration. Inference algorithms based on graph cuts and belief propagation have been found to yield accurate results, but despite recent advances are often too slow for practical use. In this paper we present some algorithmic techniques that substantially improve the running time of the loopy belief propagation approach. One of the techniques reduces the complexity of the inference algorithm to be linear rather than quadratic in the number of possible labels for each pixel, which is important for problems such as image restoration that have a large label set. Another technique speeds up and reduces the memory requirements of belief propagation on grid graphs. A third technique is a multi-grid method that makes it possible to obtain good results with a small fixed number of message passing iterations, independent of the size of the input images. Taken together these techniques speed up the standard algorithm by several orders of magnitude. In practice we obtain results that are as accurate as those of other global methods (e.g., using the Middlebury stereo benchmark) while being nearly as fast as purely local methods.

Distance Transforms of Sampled Functions

Abstract: We describe linear-time algorithms for solving a class of problems that involve transforming a cost function on a grid using spatial information. These problems can be viewed as a generalization of classical distance transforms of binary images, where the binary image is replaced by an arbitrary function on a grid. Alternatively they can be viewed in terms of the minimum convolution of two functions, which is an important operation in grayscale morphology. A consequence of our techniques is a simple and fast method for computing the Euclidean distance transform of a binary image. Our algorithms are also applicable to Viterbi decoding, belief propagation, and optimal control.