Results 1  10
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15
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 15 (3 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.
HighDensity Model for Server Allocation and Placement
 in Proc. of ACM SIGMETRICS ’02
, 2002
"... It is well known that optimal server placement is NPhard. We present an approximate model for the case when both clients and servers are dense, and propose a simple server allocation and placement algorithm based on highrate vector quantization theory. The key idea is to regard the location of a r ..."
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Cited by 13 (0 self)
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It is well known that optimal server placement is NPhard. We present an approximate model for the case when both clients and servers are dense, and propose a simple server allocation and placement algorithm based on highrate vector quantization theory. The key idea is to regard the location of a request as a random variable with probability density that is proportional to the demand at that location, and the problem of server placement as source coding, i.e., to optimally map a source value (request location) to a codeword (server location) to minimize distortion (network cost). This view has led to a joint server allocation and placement algorithm that has a timecomplexity that is linear in the number of clients. Simulations are presented to illustrate its performance.
Maintaining information in fullydynamic trees with top trees. http://arXiv.org/abs/cs/0310065
, 2003
"... We introduce top trees as a new data structure that makes it simpler to maintain many kinds of information in a fullydynamic forest. As prime examples, 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 a ..."
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Cited by 12 (0 self)
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We introduce top trees as a new data structure that makes it simpler to maintain many kinds of information in a fullydynamic forest. As prime examples, 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 can easily be derived from either 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 Sleator and Tarjan’s dynamic trees [A Data Structure for Dynamic Trees. J. Comput. Syst. Sc. 26
Placing Resources on a Growing Line
, 1998
"... We consider the problem of placing k identical resources in a graph where each vertex is associated with a nonnegative weight representing the frequency of requests issued by that vertex for the resource. We define the cost of a placement as the sum over all vertices of their distances to the closes ..."
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Cited by 6 (0 self)
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We consider the problem of placing k identical resources in a graph where each vertex is associated with a nonnegative weight representing the frequency of requests issued by that vertex for the resource. We define the cost of a placement as the sum over all vertices of their distances to the closest resource weighted by their weights. The optimal placement is the placement with least cost among all placements. We give an algorithm for placing optimally k resources on a "growing" line. The algorithm starts with an empty line. At each step a new vertex is appended to the line and the algorithm has to recompute the optimal placement of the k resources. Our algorithm processes each new vertex in O(k) amortized time. As a corollary, we obtain an algorithm that computes the optimal placement of k resources in an nvertex line in time O(kn), which is optimal for constant k.
The kMedian Problem for Directed Trees
, 2003
"... The kmedian problem is a classical facility location problem. We consider the kmedian problem for directed trees, motivated by the problem of locating proxies on the World Wide Web. The two main results of the paper are an O(n log n) time algorithm for k = 2 and an O(n log² n) time algorithm fo ..."
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Cited by 2 (1 self)
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The kmedian problem is a classical facility location problem. We consider the kmedian problem for directed trees, motivated by the problem of locating proxies on the World Wide Web. The two main results of the paper are an O(n log n) time algorithm for k = 2 and an O(n log² n) time algorithm for k = 3. The previously known upper bounds for these two cases were O(n²).
An Algorithm for the 2Median Problem on TwoDimensional Meshes
, 1999
"... We study the pmedian problem which is one the classical problems in location theory. For p = 2 and on a twodimensional mesh, we give an O(mn 2 p)time algorithm for solving the problem, where, assuming that m n, m is the number of rows of the mesh containing demand points, n the number of colum ..."
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Cited by 1 (0 self)
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We study the pmedian problem which is one the classical problems in location theory. For p = 2 and on a twodimensional mesh, we give an O(mn 2 p)time algorithm for solving the problem, where, assuming that m n, m is the number of rows of the mesh containing demand points, n the number of columns containing demand points, and p the number of demand points. 1 Introduction The mesh (and its variant, the torus) is a popular topology for processor interconnection in parallel computers. It has practical advantages such as low degree and perfectly compact layout when compared to other wellknown topologies, for example the hypercube. A notable example of parallel computers based on the mesh topology is the iWarp system [4]. Dally has shown that lowdimensional networks have lower latency and higher hotspot throughput than highdimensional networks [2]. In this paper, we study the problem of finding a 2median set in a twodimensional mesh. The pmedian problem is a wellknown problem ...