Abstract not found

We present new approximation algorithms for several facility location problems. In each facility location problem that we study, there is a set of locations at which we may build a facility (such as a warehouse), where the cost of building at location i is f i ; furthermore, there is a set of client locations (such as stores) that require to be serviced by a facility, and if a client at location j is assigned to a facility at location i, a cost of c ij is incurred. The objective is to determine a set of locations at which to open facilities so as to minimize the total facility and assignment costs. In the uncapacitated case, each facility can service an unlimited number of clients, whereas in the capacitated case, each facility can serve, for example, at most u clients. These models and a number of closely related ones have been studied extensively in the Operations Research literature. We shall consider the case in which the assignment costs are symmetric and satisfy the triangle ineq...

A fundamental facility location problem is to choose the location of facilities, such as industrial plants and warehouses, to minimize the cost of satisfying the demand for some commodity. There are associated costs for locating the facilities, as well as transportation costs for distributing the commodities. We assume that the transportation costs form a metric. This problem is commonly referred to as the uncapacitated facility location (UFL) problem. Applications to bank account location and clustering, as well as many related pieces of work, are discussed by Cornuejols, Nemhauser and Wolsey [2]. Recently, the first constant factor approximation algorithm for this problem was obtained by Shmoys, Tardos and Aardal [16]. We show that a simple greedy heuristic combined with the algorithm by Shmoys, Tardos and Aardal, can be used to obtain an approximation guarantee of 2.408. We discuss a few variants of the problem, demonstrating better approximation factors for restricted versions of the problem. We also show that the problem is Max SNP-hard. However, the inapproximability constants derived from the Max SNP hardness are very close to one. By relating this problem to Set Cover, we prove a lower bound of 1.463 on the best possible approximation ratio assuming NP / ∈ DT IME[n O(log log n)]. 1

In the k-median problem we are given a set S of n points in a metric space and a positive integer k. We desire to locate k medians in space, such that the sum of the distances from each of the points of S to the nearest median is minimized. This paper gives an approximation scheme for the plane that for any c > 0 produces a solution of cost at most 1 + 1/c times the optimum and runs in time O(n O(c+1) ). The approximation scheme also generalizes to some problems related to k-median. Our methodology is to extend Arora's [1, 2] techniques for the TSP, which hitherto seemed inapplicable to problems such as the k-median problem. 1 Introduction In the k-median problem we are given a set S of n points in a metric space and a positive integer k. We desire to locate k medians in the space, such that the sum of the distances from each of the points of S to the nearest median is minimized. Besides its intrinsic appeal as a cleanly-stated, basic unsolved problem in combinatorial optimizatio...

In this paper we present a 1.52-approximation algorithm for the metric uncapacitated facility location problem, and a 2-approximation algorithm for the metric capacitated facility location problem with soft capacities. Both these algorithms improve the best previously known approximation factor for the corresponding problem, and our soft-capacitated facility location algorithm achieves the integrality gap of the standard LP relaxation of the problem. Furthermore, we will show, using a result of Thorup, that our algorithms can be implemented in quasi-linear time.

Semistructured data is characterized by the lack of any fixed and rigid schema, although typically the data has some implicit structure. While the lack of fixed schema makes extracting semistructured data fairly easy and an attractive goal, presenting and querying such data is greatly impaired. Thus, a critical problem is the discovery of the structure implicit in semistructured data and, subsequently, the recasting of the raw data in terms of this structure. In this paper, we consider a very general form of semistructured data based on labeled, directed graphs. We show that such data can be typed using the greatest fixpoint semantics of monadic datalog programs. We present an algorithm for approximate typing of semistructured data. We establish that the general problem of finding an optimal such typing is NP-hard, but present some heuristics and techniques based on clustering that allow efficient and near-optimal treatment of the problem. We also present some preliminary experimental results.

We present a simple and natural greedy algorithm for the metric uncapacitated facility location problem achieving an approximation guarantee of 1.61 whereas the best previously known was 1.73. Furthermore, we will show that our algorithm has a property which allows us to apply the technique of Lagrangian relaxation. Using this property, we can nd better approximation algorithms for many variants of the facility location problem, such as the capacitated facility location problem with soft capacities and a common generalization of the k-median and facility location problem. We will also prove a lower bound on the approximability of the k-median problem.

XML is rapidly emerging as the new standard for data representation and exchange on the Web. An XML document can be accompanied by a Document Type Descriptor (DTD) which plays the role of a schema for an XML data collection. DTDs contain valuable information on the structure of documents and thus have a crucial role in the efficient storage of XML data, as well as the effective formulation and optimization of XML queries. In this paper, we propose XTRACT, a novel system for inferring a DTD schema for a database of XML documents. Since the DTD syntax incorporates the full expressive power of regular expressions, naive approaches typically fail to produce concise and intuitive DTDs. Instead, the XTRACT inference algorithms employ a sequence of sophisticated steps that involve: (1) finding patterns in the input sequences and replacing them with regular expressions to generate "general" candidate DTDs, (2) factoring candidate DTDs using adaptations of algorithms from the logic optimization...

We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861. The running time of our algorithm is O(m log m), where m is the total number of edges in the underlying complete bipartite graph between cities and facilities. We use our algorithm to improve recent results for some variants of the problem, such as the fault tolerant and outlier versions. In addition, we introduce a new variant which can be seen as a special case of the concave cost version of this problem.

) Moses Charikar Samir Khuller y David M. Mount z Giri Narasimhan x Abstract Facility location problems are traditionally investigated with the assumption that all the clients are to be provided service. A significant shortcoming of this formulation is that a few very distant clients, called outliers, can exert a disproportionately strong influence over the final solution. In this paper we explore a generalization of various facility location problems (K-center, K-median, uncapacitated facility location etc) to the case when only a specified fraction of the customers are to be served. What makes the problems harder is that we have to also select the subset that should get service. We provide generalizations of various approximation algorithms to deal with this added constraint. 1 Introduction The facility location problem and the related clustering problems, k-median and k-center, are widely studied in operations research and computer science [3, 7, 22, 24, 32]. Typically in...