Mordecai J. Golin

On the optimal placement of web proxies in the Internet

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.

Competitive facility location: the Voronoi game

Abstract. We consider a competitive facility location problem with two players.Pla yers alternate placing points, one at a time, into the playing arena, until each of them has placed n points.The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins.W e present a winning strategy for the second player, where the arena is a circle or a line segment.

Meeting the Welch and Karystinos-Pados Bounds on DS-CDMA Binary Signature Sets

The Welch lower bound on the total-squared-correlation (TSC) of binary signature sets is loose for binary signature sets whose length L is not a multiple of 4. Recently Karystinos and Pados [6,7] developed new bounds that are better than the Welch bound in those cases, and showed how to achieve the bounds with modified Hadamard matrices except in a couple of cases. In this paper, we study the open cases.

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

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

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.

Mellin transforms and asymptotics

Mellin transforms and Dirichlet series are useful in quantifying periodicity phenomena present in recursive divide-and-conquer algorithms. This note illustrates the techniques by providing a precise analysis of the standard topdown recursive mergesort algorithm, in the average case, as well as in the worst and best cases. It also derives the variance and shows that the cost of mergesort has a Gaussian limiting distribution. The approach is applicable to a number of divide-and-conquer recurrences.

The number of spanning trees in circulant graphs

Abstract In this paper we develop a method for determining the exact number of spanning trees in (directed or undirected) circulant graphs. Using this method we can, for any class of circulant graph, exhibit a recurrence relation for the number of its spanning trees. We describe the method and give examples of its use.

Curve reconstruction from noisy samples

We present an algorithm to reconstruct a collection of disjoint smooth closed curves from n noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation of each point in the normal direction with a magnitude smaller than the minimum local feature size. The reconstruction is faithful with a probability that approaches 1 as n increases.We expect that our approach can lead to provable algorithms under less restrictive noise models and for handling non-smooth features.

An algorithm for finding a K -median in a directed tree

Abstract We consider the problem of finding a k -median in a directed tree. We present an algorithm that computes a k -median in O (Pk 2 ) time where k is the number of resources to be placed and P is the path length of the tree. In the case of a balanced tree, this implies O (k 2 n log n) time, in a random tree O (k 2 n 3/2 ), while in the worst case O (k 2 n 2 ) . Our method employs dynamic programming and uses O (nk) space, while the best known algorithms for undirected trees require O (n 2 k) space.

On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes

It is well known that the complexity, i.e. the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as Θ(n2). It is also known that if the points are chosen Independently Identically Distributed uniformly from a 3-dimensional region such as a cube or sphere, then the expected complexity falls to O(n). In this paper we introduce the problem of analyzing what occurs if the points are chosen from a 2-dimensional region in 3-dimensional space. As an example, we examine the situation when the points are drawn from a Poisson distribution with rate n on the surface of a convex polytope. We prove that, in this case, the expected complexity of the resulting Voronoi diagram is O(n).