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12
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 423 (21 self)
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We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization problems fit in this framework, including the shortest path, minimumcost spanning tree, minimumweight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most of these problems. For instance, we obtain a 2approximation algorithm for the minimumweight perfect matching problem under the triangle inequality. Our running time of O(n log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n 3) time for dense graphs. A similar result is obtained for the 2matching problem and its variants. We also derive the first approximation algorithms for many NPcomplete problems, including the nonfixed pointtopoint connection problem, the exact path partitioning problem, and complex locationdesign problems. Moreover, for the prizecollecting traveling salesman or Steiner tree problems, we obtain 2approximation algorithms, therefore improving the previously bestknown performance guarantees of 2.5 and 3, respectively [Math. Programming, 59 (1993), pp. 413420].
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 143 (5 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.
Approximation Algorithms for Minimum Tree Partition
 Disc. Applied Math
, 1998
"... We consider a problem of locating communication centers. In this problem, it is required to partition the set of n customers into subsets minimizing the length of nets required to connect all the customers to the communication centers. Suppose that communication centers are to be placed in p of the ..."
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Cited by 4 (3 self)
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We consider a problem of locating communication centers. In this problem, it is required to partition the set of n customers into subsets minimizing the length of nets required to connect all the customers to the communication centers. Suppose that communication centers are to be placed in p of the customers locations. The number of customers each center supports is also given. The problem remains to divide a graph into sets of the given sizes, keeping the sum of the spanning trees minimal. The problem is NPComplete, and no polynomial algorithm with bounded error ratio can be given, unless P = NP . We present an approximation algorithm for the problem assuming that the edge lengths satisfy the triangle inequality. It runs in O(p 2 4 p +n 2 ) time (n = jV j) and comes within a factor of 2p \Gamma 1 of optimal. When the sets' sizes are all equal this algorithm runs in O(n 2 ) time. Next an improved algorithm is presented which obtains as an input a positive integer x (x n \Gamm...
Communication
, 2005
"... www.elsevier.com/locate/dam A class of heuristics for the constrained forest problem ..."
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Cited by 3 (0 self)
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www.elsevier.com/locate/dam A class of heuristics for the constrained forest problem
Approximation Bounds for Minimum Information Loss Microaggregation
, 2009
"... The NPhard microaggregation problem seeks a partition of data points into groups of minimum specified size k, so as to minimize the sum of the squared euclidean distances of every point to its group’s centroid. One recent heuristic provides an Oðk 3 Þ guarantee for this objective function and an O ..."
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Cited by 1 (1 self)
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The NPhard microaggregation problem seeks a partition of data points into groups of minimum specified size k, so as to minimize the sum of the squared euclidean distances of every point to its group’s centroid. One recent heuristic provides an Oðk 3 Þ guarantee for this objective function and an Oðk 2 Þ guarantee for a version of the problem that seeks to minimize the sum of the distances of the points to its group’s centroid. This paper establishes approximation bounds for another microaggregation heuristic, providing better approximation guarantees of Oðk 2 Þ for the squared distance measure and OðkÞ for the distance measure.
D.P.: A dualfitting 32 approximation algorithm for some minimumcost graph problems
 Algorithms – ESA 2012, 20th Annual European Symposium, no. 7501 in Lecture Notes in Computer Science
, 2012
"... Abstract. In an ESA 2011 paper, Couëtoux [2] gives a beautiful 3 ..."
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Abstract. In an ESA 2011 paper, Couëtoux [2] gives a beautiful 3
Mathematical Programming Series B manuscript No. (will be inserted by the editor) A 32Approximation Algorithm for Some MinimumCost Graph
"... Abstract We consider a class of graph problems introduced in a paper of Goemans and Williamson that involve finding forests of minimum edge cost. This class includes a number of location/routing problems; it also includes a problem in which we are given as input a parameter k, and want to find a fo ..."
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Abstract We consider a class of graph problems introduced in a paper of Goemans and Williamson that involve finding forests of minimum edge cost. This class includes a number of location/routing problems; it also includes a problem in which we are given as input a parameter k, and want to find a forest such that each component has at least k vertices. Goemans and Williamson gave a 2approximation algorithm for this class of problems. We give an improved 32approximation algorithm. 1
Letters
, 2004
"... www.elsevier.com/locate/orl Another greedy heuristic for the constrained forest problem ..."
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www.elsevier.com/locate/orl Another greedy heuristic for the constrained forest problem