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41
Facility Location under Uncertainty: A Review
 IIE Transactions
, 2004
"... Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made th ..."
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Cited by 33 (6 self)
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Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made the development of models for facility location under uncertainty a high priority for researchers in both the logistics and stochastic/robust optimization communities. Indeed, a large number of the approaches that have been proposed for optimization under uncertainty have been applied to facility location problems. This paper reviews the literature...
Maintaining Center and Median in Dynamic Trees
, 2000
"... We show how to maintain centers and medians for a collection of dynamic trees where edges may be inserted and deleted and node and edge weights may be changed. All updates are supported in O(log n) time, where n is the size of the tree(s) involved in the update. ..."
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Cited by 17 (4 self)
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We show how to maintain centers and medians for a collection of dynamic trees where edges may be inserted and deleted and node and edge weights may be changed. All updates are supported in O(log n) time, where n is the size of the tree(s) involved in the update.
Continuous Weber and kMedian Problems
, 2000
"... We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the "continuous kmedian (Weber) problem" where the goal is to select one or more center points that minimize the average d ..."
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Cited by 13 (2 self)
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We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the "continuous kmedian (Weber) problem" where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed as an integral over the relevant region, versus the usual discrete sum of distances. The resulting facility location problems are inherently geometric, requiring analysis techniques of computational geometry. We provide polynomialtime algorithms for various versions of the L1 1median (Weber) problem. We also consider the multiplecenter version of the L1 kmedian problem, which we prove is NPhard for large k.
Maintaining information in fullydynamic trees with top trees
 ACM Transactions on Algorithms
, 2003
"... We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fullydynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we show how to maintain the diameter, center, and median of eac ..."
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Cited by 12 (0 self)
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We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fullydynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we show how to maintain the diameter, center, and median of each tree in the forest. The forest can be updated by insertion and deletion of edges and by changes to vertex and edge weights. Each update is supported in O(log n) time, where n is the size of the tree(s) involved in the update. Also, we show how to support nearest common ancestor queries and level ancestor queries with respect to arbitrary roots in O(log n) time. Finally, with marked and unmarked vertices, we show how to compute distances to a nearest marked vertex. The later has applications to approximate nearest marked vertex in general graphs, and thereby to static optimization problems over shortest path metrics. Technically speaking, top trees are easily implemented either with Frederickson’s topology trees [Ambivalent Data Structures for Dynamic 2EdgeConnectivity and k Smallest Spanning Trees, SIAM J. Comput. 26 (2) pp. 484–538, 1997] or with Sleator and Tarjan’s dynamic
Word of Mouth: Rumor Dissemination in Social Networks
"... Abstract. In this paper we examine the diffusion of competing rumors in social networks. Two players select a disjoint subset of nodes as initiators of the rumor propagation, seeking to maximize the number of persuaded nodes. We use concepts of game theory and location theory and model the selection ..."
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Cited by 12 (1 self)
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Abstract. In this paper we examine the diffusion of competing rumors in social networks. Two players select a disjoint subset of nodes as initiators of the rumor propagation, seeking to maximize the number of persuaded nodes. We use concepts of game theory and location theory and model the selection of starting nodes for the rumors as a strategic game. We show that computing the optimal strategy for both the first and the second player is NPcomplete, even in a most restricted model. Moreover we prove that determining an approximate solution for the first player is NPcomplete as well. We analyze several heuristics and show that—counterintuitively—being the first to decide is not always an advantage, namely there exist networks where the second player can convince more nodes than the first, regardless of the first player’s decision. 1
A Maximum bMatching Problem Arising From Median Location Models With Applications To The Roommates Problem
 Mathematical Programming
, 1995
"... . We consider maximum bmatching problems where the nodes of the graph represent points in a metric space, and the weight of an edge is the distance between the respective pair of points. We show that if the space is either the rectilinear plane, or the metric space induced by a tree network, then ..."
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Cited by 11 (2 self)
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. We consider maximum bmatching problems where the nodes of the graph represent points in a metric space, and the weight of an edge is the distance between the respective pair of points. We show that if the space is either the rectilinear plane, or the metric space induced by a tree network, then the bmatching problem is the dual of the (single) median location problem with respect to the given set of points. This result does not hold for the Euclidean plane. However, we show that in this case the bmatching problem is the dual of a median location problem with respect to the given set of points, in some extended metric space. We then extend this latter result to any geodesic metric in the plane. The above results imply that the respective fractional bmatching problems have integer optimal solutions. We use these duality results to prove the nonemptiness of the core of a cooperative game defined on the roommate problem corresponding to the above matching model. 1. Introduction. ...
The complexity of constructing evolutionary trees using experiments
, 2001
"... We present tight upper and lower bounds for the problem of constructing evolutionary trees in the experiment model. We describe an algorithm which constructs an evolutionary tree of n species in time O(nd log d n) using at most n⌈d/2⌉(log 2⌈d/2⌉−1 n+O(1)) experiments for d> 2, and at most n(log n+ ..."
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Cited by 8 (1 self)
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We present tight upper and lower bounds for the problem of constructing evolutionary trees in the experiment model. We describe an algorithm which constructs an evolutionary tree of n species in time O(nd log d n) using at most n⌈d/2⌉(log 2⌈d/2⌉−1 n+O(1)) experiments for d> 2, and at most n(log n+O(1)) experiments for d = 2, where d is the degree of the tree. This improves the previous best upper bound by a factor Θ(log d). For d = 2 the previously best algorithm with running time O(n log n) had a bound of 4n log n on the number of experiments. By an explicit adversary argument, we show an Ω(nd log d n) lower bound, matching our upper bounds and improving the previous best lower bound by a factor Θ(log d n). Central to our algorithm is the construction and maintenance of separator trees of small height, which may be of independent interest.
Multicriteria Network Location Problems with Sum Objectives
, 1996
"... In this paper network location problems with several objectives are discussed, where every single objective is a classical median objective function. We will look at the problem of finding Pareto optimal locations and lexicographically optimal locations. It is shown that for Pareto optimal locations ..."
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Cited by 7 (4 self)
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In this paper network location problems with several objectives are discussed, where every single objective is a classical median objective function. We will look at the problem of finding Pareto optimal locations and lexicographically optimal locations. It is shown that for Pareto optimal locations in undirected networks no node dominance result can be shown. Structural results as well as efficient algorithms for these multicriteria problems are developed. In the special case of a tree network a generalization of Goldman's dominance algorithm for finding Pareto locations is presented.
Robust Location Problems with Pos/Neg Weights on a Tree
 Networks
, 1999
"... . In this paper we consider different aspects of robust 1median problems on a tree network with uncertain or dynamically changing edge lengths and vertex weights which can also take negative values. The dynamic nature of a parameter is modeled by a linear function of time. A linear algorithm is ..."
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Cited by 7 (0 self)
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. In this paper we consider different aspects of robust 1median problems on a tree network with uncertain or dynamically changing edge lengths and vertex weights which can also take negative values. The dynamic nature of a parameter is modeled by a linear function of time. A linear algorithm is designed for the absolute dynamic robust 1median problem on a tree. The dynamic robust deviation 1median problem on a tree with n vertices can be solved in O(n 2 ff(n) log n) time. Both problems possess optimal solutions which are not vertices of the graph (contradicting a statement of Kouvelis and Yu). The uncertainty is modeled by given intervals, in which each parameter can take a value randomly. The robust 1median problem with interval data, where vertex weights might be negative, can be solved in linear time. The corresponding deviation problem can be solved in O(n 2 ) time. Keywords: Location problems, robust optimization, median problem, obnoxious facilities 1 Intro...
Finding Cores of Limited Length
, 2001
"... In this paper we consider several wellstudied variants of the problem of finding a core of a prescribed length in a tree. Here a core is a path minimizing the sum of the distances to all nodes in the tree. Our most general result is an O(n log n α(n)) algorithm for the case with weighted tree edges ..."
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Cited by 6 (0 self)
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In this paper we consider several wellstudied variants of the problem of finding a core of a prescribed length in a tree. Here a core is a path minimizing the sum of the distances to all nodes in the tree. Our most general result is an O(n log n α(n)) algorithm for the case with weighted tree edges. The previous best bound was O(n³) due to Minieka (Networks, 1985).