There is an increasing need to quickly and efficiently learn network distances, in terms of metrics such as latency or bandwidth, between Internet hosts. For example, Internet content providers often place data and server mirrors throughout the Internet to improve access latency for clients, and it is necessary to direct clients to the closest mirrors based on some distance metric in order to realize the benefit of mirrors. We suggest a scalable Internet-wide architecture, called IDMaps, which measures and disseminates distance information on the global Internet. Higher-level services can collect such distance information to build a virtual distance map of the Internet and estimate the distance between any pair of IP addresses. We present our solutions to the measurement server placement and distance map construction problems in IDMaps. We show that IDMaps can indeed provide useful distance estimations to applications such as closest-mirror selection. 1 Keywords: network service, distributed algorithms, scalability, modeling. 1

In this paper we present a genetic algorithm-based heuristic for non-unicost set covering problems. We propose several modifications to the basic genetic procedures including a new fitness-based crossover operator (fusion), a variable mutation rate and a heuristic feasibility operator tailored specifically for the set covering problem. The performance of our algorithm was evaluated on a large set of randomly generated problems. Computational results showed that the genetic algorithm-based heuristic is capable of producing high-quality solutions. Keywords: genetic algorithms; set covering; optimisation. 1 Introduction The set covering problem (SCP) is the problem of covering the rows of a m-row, n- column, zero-one matrix (a ij ) by a subset of the columns at minimal cost. Defining x j = 1 if column j (with cost c j ? 0) is in the solution and x j = 0 otherwise, the SCP is Minimise n X j=1 c j x j (1) Subject to n X j=1 a ij x j 1, i = 1; : : : ; m (2) x j 2 f0; 1g, j = 1; ...

Data replication is used extensively in wide-area distributed systems to achieve low data-access latency. A large number of heuristics have been proposed to perform replica placement. Practical experience indicates that the choice of heuristic makes a big difference in terms of the cost of required infrastructure (e.g., storage capacity and network bandwidth), depending on system topology, workload and performance goals.

The capacitated K-center problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may be assigned at most L vertices. This problem is known to be NP-hard. We give polynomial time approximation algorithms for two different versions of this problem that achieve approximation factors of 5 and 6. We also study some generalizations of this problem. 1. Introduction The basic K-center problem is a fundamental facility location problem [17] and is defined as follows: given an edge-weighted graph G = (V; E) find a subset S ` V of size at most K such that each vertex in V is "close" to some vertex in S. More formally, the objective function is defined as follows: min S`V max u2V min v2S d(u; v) where d is the distance function. For example, one may wish to install K fire stations and mi...

Two of the fundamental questions that arise in the manufacturing industry concerning every type of manufacturing process are: 1. Given an object, can it be built using a particular process? 2. Given that an object can be built using a particular process, what is the best way to construct the object? The latter question gives rise to many different problems depending on how best is qualified. We address these problems for two complimentary categories of manufacturing processes: rapid prototyping systems and casting processes. The method we use to address these problems is to first define a geometric model of the process in question and then answer the questions on that model. In the category of rapid prototyping systems, we concentrate on stereolithography, which is emerging as one of the most popular rapid prototyping systems. We model stereolithography geometrically and then study the class of objects that admit a construction in this model. For the objects that admit a constructio...

In the present dissertation we investigate structural and algorithmic aspects of the frequency assignment problem in mobile telephone networks. This problem is of particular interest for the graph theory because of its close relationship to graph coloring. The frequency assignment problem includes the characteristic features of T-coloring, list coloring, and set coloring, and belongs thereby to NP-hard combinatorial problems. The main part of this thesis is dedicated to the so-called hybrid networks, with some stations operating according to the static principle and other stations according to the dynamic principle. We develop a graph-theoretical model and introduce two optimization criteria for the frequency assignment problem in hybrid networks. The computational complexity of evaluating these criteria is first examined for graphs with bounded treewidth and for complete graphs. In the further investigations we concentrate on the criterion called channel stability number, which genera...

A new combinatorial approach for modelling and reconstructing sibling relationships in a single generation of individuals without parental information is proposed in this paper. Simple genetic constraints on the full-sibling groups, imposed by the Mendelian inheritance rules, are employed to investigate data from codominant DNA markers. To extract the minimum number of biologically consistent sibling groups, the proposed combinatorial approach is employed to formulate this minimization problem as a set covering problem, which is a well-known NP-hard combinatorial optimization problem. We conducted a simulation study of a relaxed version of the proposed algorithm to demonstrate that our combinatorial approach is reasonably accurate and the exact version of the sibling relationship construction algorithm should be pursued. In addition, the results of this study suggest that the proposed algorithm will pave our way to a new approach in computational population genetics as it does not require any a priori knowledge about allele frequency, population size, mating system or family size distributions to reconstruct sibling relationships.

In the manufacturing industry, finding a suitable location for the pin gate (the pin gate is the point from which liquid is poured or injected into a mold) is a difficult problem when viewed from the fluid dynamics of the molding process. However, experience has shown that a suitable pin gate location possesses several geometric characteristics, namely the distance from the pin gate to any point in the mold should be small and the number of turns on the path from a point in the mold to the pin gate should be small. We address the problem of computing locations that possess these geometric characteristics. Given a mold M (modeled by an n vertex simple polygon) we show how to compute the Euclidean center of M constrained to lie in the interior of M or on the boundary of M in O(n log n+k) time where k is the number of intersections between M and the furthest point Voronoi diagram of the vertices of M . We show how to compute the geodesic center of M constrained to the boundary in O(n log n) time and the geodesic center of M constrained to lie in a polygonal region in O(n(n + k)) time. Finally, we show how to compute the link center of M constrained to the boundary of M in O(n log n) time.

Facility location problems have always been studied with the assumption that the edge lengths in the network are static and do not change over time. The underlying network could be used to model a city street network for emergency facility location/hospitals, or an electronic network for locating information centers. In any case, it is clear that due to traffic congestion the traversal time on links changes with time. Very often, we have some estimates as to how the edge lengths change over time, and our objective is to choose a set of locations (vertices) as centers, such that at every time instant each vertex has a center close to it (clearly, the center close to a vertex may change over time). We also provide approximation algorithms as well as hardness results for the K-center problem under this model. This is the first comprehensive study regarding approximation algorithms for facility location for good time-invariant solutions. 1. Introduction Previous theoretical work on fac...

MC routing protocols currently being standardized, PIM and CBT, propose the use of shared center-based trees, but they do not specify how to select the centers of these trees. We survey previous work on the center selection problems in the fields of operations research and communication networks. 1