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Applying parallel computation algorithms in the design of serial algorithms
 J. ACM
, 1983
"... Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for design ..."
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Cited by 238 (7 self)
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Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for designing an efficient serial algorithm for another problem. A d ~ eframework d for cases like this is presented. Particular cases, which are discussed in this paper, provide motivation for examining parallelism in sorting, selection, minimumspanningtree, shortest route, maxflow, and matrix multiplication problems, as well as in scheduling and locational problems.
ON THE COMPLEXITY OF SOME COMMON GEOMETRIC LOCATION PROBLEMS
 SIAM J. COMPUTING
, 1984
"... Given n demand points in the plane, the pcenter problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demo & point to its respective nearest supply point. The pmedian problem is to minimize the sum of distances from demand points to their resp ..."
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Cited by 121 (1 self)
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Given n demand points in the plane, the pcenter problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demo & point to its respective nearest supply point. The pmedian problem is to minimize the sum of distances from demand points to their respective nearest supply points. We prove that the pcenter and the pmedia problems relative to both the Euclidean and the rectilinear metrics are NPhard. In fact, we prove that it is NPhard even to approximate the pcenter problems sufficiently closely. The reductions are from 3satisfiability.
THE MAXIMUM COVERAGE LOCATION PROBLEM*
"... Abstract. In this paper we define and discuss the following problem which we call the maximum coverage location problem. A transportation network is given together with the locations of customers and facilities. Thus, for each customer i, a radius ri is known such that customer i can currently be se ..."
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Abstract. In this paper we define and discuss the following problem which we call the maximum coverage location problem. A transportation network is given together with the locations of customers and facilities. Thus, for each customer i, a radius ri is known such that customer i can currently be served by a facility which is located within a distance of r, from the location of customer i. We consider the problem from the point of view of a new company which is interested in establishing new facilities on the network so as to maximize the company's &quot;share of the market. &quot; Specifically, assume that the company gains an amount of wi in case customer i decides to switch over to one of the new facilities. Moreover, we assume that the decision to switch over is based on proximity only, i.e., customer i switches over to a new facility only if the latter is located at a distance less than ri from i. The problem is to locate p new facilities so as to maximize the total gain. The maximum coverage problem is a relatively complicated one even on treenetworks. This is because one aspect of the problem is the selection of the subset of customers to be taken over. Nevertheless, we present an O(nZp) algorithm for this problem on a tree. Our approach can be applied to other similar problems which are discussed in the paper. 1. Introduction. We
7Joint Cluster Analysis of Attribute Data and Relationship Data: The Connected kCenter Problem, Algorithms and Applications
"... Attribute data and relationship data are two principal types of data, representing the intrinsic and extrinsic properties of entities. While attribute data have been the main source of data for cluster analysis, relationship data such as social networks or metabolic networks are becoming increasingl ..."
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Attribute data and relationship data are two principal types of data, representing the intrinsic and extrinsic properties of entities. While attribute data have been the main source of data for cluster analysis, relationship data such as social networks or metabolic networks are becoming increasingly available. It is also common to observe both data types carry complementary information such as in market segmentation and community identification, which calls for a joint cluster analysis of both data types so as to achieve better results. In this article, we introduce the novel Connected kCenter (CkC) problem, a clustering model taking into account attribute data as well as relationship data. We analyze the complexity of the problem and prove its NPhardness. Therefore, we analyze the approximability of the problem and also present a constant factor approximation algorithm. For the special case of the CkC problem where the relationship data form a tree structure, we propose a dynamic programming method giving an optimal solution in polynomial time. We further present NetScan, a heuristic algorithm that is efficient and effective for large real databases. Our extensive experimental evaluation on real datasets demonstrates the meaningfulness and accuracy of the