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159
THE PRIMALDUAL METHOD FOR APPROXIMATION ALGORITHMS AND ITS APPLICATION TO NETWORK DESIGN PROBLEMS
"... The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent researc ..."
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Cited by 124 (7 self)
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The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent research applying the primaldual method to problems in network design.
A Comparison of Labeling Schemes for Ancestor Queries
, 2002
"... Motivated by a recent application in XML search engines we study the problem of labeling the nodes of a tree (XML file) such that given the labels of two nodes one can determine whether one node is an ancestor of the other. We describe several new prefixbased labeling schemes, where an ancestor que ..."
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Cited by 115 (8 self)
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Motivated by a recent application in XML search engines we study the problem of labeling the nodes of a tree (XML file) such that given the labels of two nodes one can determine whether one node is an ancestor of the other. We describe several new prefixbased labeling schemes, where an ancestor query roughly amounts to testing whether one label is a prefix of the other. We compare our new schemes to a simple intervalbased scheme currently used by search engines, as well as, to schemes with the best theoretical guarantee on the maximum label length. We performed our experimental evaluation on real XML data and on some families of random trees.
Nearly Linear Time Approximation Schemes for Euclidean TSP and other Geometric Problems
, 1997
"... We present a randomized polynomial time approximation scheme for Euclidean TSP in ! 2 that is substantially more efficient than our earlier scheme in [2] (and the scheme of Mitchell [21]). For any fixed c ? 1 and any set of n nodes in the plane, the new scheme finds a (1+ 1 c )approximation to ..."
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Cited by 95 (3 self)
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We present a randomized polynomial time approximation scheme for Euclidean TSP in ! 2 that is substantially more efficient than our earlier scheme in [2] (and the scheme of Mitchell [21]). For any fixed c ? 1 and any set of n nodes in the plane, the new scheme finds a (1+ 1 c )approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. (Our earlier scheme ran in n O(c) time.) For points in ! d the algorithm runs in O(n(log n) (O( p dc)) d\Gamma1 ) time. This time is polynomial (actually nearly linear) for every fixed c; d. Designing such a polynomialtime algorithm was an open problem (our earlier algorithm in [2] ran in superpolynomial time for d 3). The algorithm generalizes to the same set of Euclidean problems handled by the previous algorithm, including Steiner Tree, kTSP, kMST, etc, although for kTSP and kMST the running time gets multiplied by k. We also use our ideas to design nearlylinear time approximation schemes for Euclidean vers...
Computing MinimumWeight Perfect Matchings
 INFORMS
, 1999
"... We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the ..."
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Cited by 90 (2 self)
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We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual dualchange � for each tree. As a benchmark of the algorithm’s performance, solving a 100,000node geometric instance on a 200 Mhz PentiumPro computer takes approximately 3 minutes.
Nearest Common Ancestors: A survey and a new distributed algorithm
, 2002
"... Several papers describe linear time algorithms to preprocess a tree, such that one can answer subsequent nearest common ancestor queries in constant time. Here, we survey these algorithms and related results. A common idea used by all the algorithms for the problem is that a solution for complete ba ..."
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Cited by 80 (11 self)
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Several papers describe linear time algorithms to preprocess a tree, such that one can answer subsequent nearest common ancestor queries in constant time. Here, we survey these algorithms and related results. A common idea used by all the algorithms for the problem is that a solution for complete balanced binary trees is straightforward. Furthermore, for complete balanced binary trees we can easily solve the problem in a distributed way by labeling the nodes of the tree such that from the labels of two nodes alone one can compute the label of their nearest common ancestor. Whether it is possible to distribute the data structure into short labels associated with the nodes is important for several applications such as routing. Therefore, related labeling problems have received a lot of attention recently.
Graph partitioning for high performance scientific simulations. Computing Reviews 45(2
, 2004
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Dynamic LCA queries on trees
 SIAM Journal on Computing
, 1999
"... Abstract. We show how to maintain a data structure on trees which allows for the following operations, all in worstcase constant time: 1. insertion of leaves and internal nodes, 2. deletion of leaves, 3. deletion of internal nodes with only one child, 4. determining the least common ancestor of any ..."
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Cited by 46 (0 self)
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Abstract. We show how to maintain a data structure on trees which allows for the following operations, all in worstcase constant time: 1. insertion of leaves and internal nodes, 2. deletion of leaves, 3. deletion of internal nodes with only one child, 4. determining the least common ancestor of any two nodes. We also generalize the Dietz–Sleator “cupfilling ” scheduling methodology, which may be of independent interest.
Approximation Algorithms for Maximum Dispersion
 Operations Research Letters
, 1997
"... : We describe approximation algorithms with bounded performance guarantees for the following problem: A graph is given with edge weights satisfying the triangle inequality, together with two numbers k and p. Find k disjoint subsets of p vertices each, so that the total weight of edges within subse ..."
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Cited by 39 (5 self)
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: We describe approximation algorithms with bounded performance guarantees for the following problem: A graph is given with edge weights satisfying the triangle inequality, together with two numbers k and p. Find k disjoint subsets of p vertices each, so that the total weight of edges within subsets is maximized. Subject Classification: Analysis of algorithms 011; heuristics 485. 1 Introduction Given is an undirected complete graph G = (V; E), with a vertex set V = fv 1 ; v 2 ; :::; v n g. Each edge (v i ; v j ) is associated with a nonnegative weight w(v i ; v j ). It is assumed that the edge weights satisfy the triangle inequality. For a subset V 0 ae V we denote by E(V 0 ) the set of edges in the complete subgraph induced by V 0 . Given p 2 f2; : : : ; ng, and k 2 1; : : : ; bn=pc, we consider the problem of finding k disjoint subsets P 1 : : : ; P k of V , with jP i j = p; i = 1; : : : ; k, such that P k i=1 P (x;y)2E(P i ) w(x; y) is maximized. This problem and some...
A PriceAnticipating Resource Allocation Mechanism for Distributed Shared
 Clusters”, 6th ACM Conference on Electronic Commerce
, 2005
"... In this paper we formulate the fixed budget resource allocation game to understand the performance of a distributed marketbased resource allocation system. Multiple users decide how to distribute their budget (bids) among multiple machines according to their individual preferences to maximize their ..."
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Cited by 38 (7 self)
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In this paper we formulate the fixed budget resource allocation game to understand the performance of a distributed marketbased resource allocation system. Multiple users decide how to distribute their budget (bids) among multiple machines according to their individual preferences to maximize their individual utility. We look at both the efficiency and the fairness of the allocation at the equilibrium, where fairness is evaluated through the measures of utility uniformity and envyfreeness. We show analytically and through simulations that despite being highly decentralized, such a system converges quickly to an equilibrium and unlike the social optimum that achieves high efficiency but poor fairness, the proposed allocation scheme achieves a nice balance of high degrees of efficiency and fairness at the equilibrium. 1.