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48
When trees collide: An approximation algorithm for the generalized Steiner problem on networks
, 1994
"... We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair fi; jg of nodes, an edgeconnectivity requirement r ij . The goal is to find a minimumcost network using the a ..."
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Cited by 219 (32 self)
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We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with linkcosts and, for each pair fi; jg of nodes, an edgeconnectivity requirement r ij . The goal is to find a minimumcost network using the available links and satisfying the requirements. Our algorithm outputs a solution whose cost is within 2dlog 2 (r + 1)e of optimal, where r is the highest requirement value. In the course of proving the performance guarantee, we prove a combinatorial minmax approximate equality relating minimumcost networks to maximum packings of certain kinds of cuts. As a consequence of the proof of this theorem, we obtain an approximation algorithm for optimally packing these cuts; we show that this algorithm has application to estimating the reliability of a probabilistic network.
Multicast Routing for Multimedia Communication
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1993
"... We present heuristics for multicast tree construction for communication that depends on: i) bounded endtoend delay along the paths from source to each destination, and ii) minimum cost of the multicast tree, where edge cost and edge delay can be independent metrics. This problem of computing such ..."
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Cited by 189 (9 self)
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We present heuristics for multicast tree construction for communication that depends on: i) bounded endtoend delay along the paths from source to each destination, and ii) minimum cost of the multicast tree, where edge cost and edge delay can be independent metrics. This problem of computing such a constrained multicast tree is NPcomplete. We show that the heuristics demonstrate good average case behavior in terms of cost, as determined through simulations on a large number of graphs.
Greedy Randomized Adaptive Search Procedures For The Steiner Problem In Graphs
 QUADRATIC ASSIGNMENT AND RELATED PROBLEMS, VOLUME 16 OF DIMACS SERIES ON DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1999
"... We describe four versions of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions of general instances of the Steiner Problem in Graphs. Di#erent construction and local search algorithms are presented. Preliminary computational results with one of the versions ..."
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Cited by 105 (29 self)
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We describe four versions of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions of general instances of the Steiner Problem in Graphs. Di#erent construction and local search algorithms are presented. Preliminary computational results with one of the versions on a variety of test problems are reported. On the majority of instances from the ORLibrary, a set of standard test problems, the GRASP produced optimal solutions. On those that optimal solutions were not found, the GRASP found good quality approximate solutions.
A nearly bestpossible approximation algorithm for nodeweighted Steiner trees
, 1993
"... We give the first approximation algorithm for the nodeweighted Steiner tree problem. Its performance guarantee is within a constant factor of the best possible unless ~ P ' NP . Our algorithm generalizes to handle other network design problems. ..."
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Cited by 104 (8 self)
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We give the first approximation algorithm for the nodeweighted Steiner tree problem. Its performance guarantee is within a constant factor of the best possible unless ~ P ' NP . Our algorithm generalizes to handle other network design problems.
The Steiner problems with edge lengths 1 and 2
 INFORMATION PROCESSING LETTERS
, 1989
"... The Steiner problem on networks asks for a shortest subgraph spanning a given subset of distinguished vertices. We give a 4/3approximation algorithm for the special case in which the underlying network is complete and all edge lengths are either 1 or 2. We also relate the Steiner problem to a compl ..."
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Cited by 77 (1 self)
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The Steiner problem on networks asks for a shortest subgraph spanning a given subset of distinguished vertices. We give a 4/3approximation algorithm for the special case in which the underlying network is complete and all edge lengths are either 1 or 2. We also relate the Steiner problem to a complexity class recently defined by Papadimitriou and Yannakakis by showing that this special case is MAX SNPhard, which may be evidence that the Steiner problem on networks has no polynomialtime approximation scheme.
Multicast Tree Generation in Networks with Asymmetric Links
 IEEE/ACM Transactions on Networking
, 1996
"... We formulate the problem of multicast tree generation as one of computing a directed Steiner tree of minimal cost. In this context, we present a polynomialtime algorithm that provides for tradeoff selection, using a single parameter , between the treecost (Steiner cost) and the runtime efficiency ..."
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Cited by 74 (0 self)
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We formulate the problem of multicast tree generation as one of computing a directed Steiner tree of minimal cost. In this context, we present a polynomialtime algorithm that provides for tradeoff selection, using a single parameter , between the treecost (Steiner cost) and the runtime efficiency. Further, the same algorithm may be used for delay optimization or treecost minimization simply by configuring the value of appropriately. We present theoretical and experimental analysis characterizing the problem and the performance of our algorithm. Theoretically, we (1) show that it is highly unlikely that there exists a polynomialtime algorithm with a performance guarantee of constant times optimum cost, (2) introduce metrics for measuring the asymmetry of graphs, and (3) show that the worstcase cost of the tree produced by our algorithm is at most twice the optimum cost times the asymmetry, for two of these asymmetry metrics. For graphs with bounded asymmetry, this gives constant ...
Improved Methods for Approximating Node Weighted Steiner Trees and Connected Dominating Sets
 Information and Computation
, 1999
"... A greedy approximation algorithm based on \spider decompositions " was developed by Klein and Ravi for node weighted Steiner trees. This algorithm provides a worst case approximation ratio of 2 ln k, where k is the number of terminals. However, the best known lower bound on the approximation ra ..."
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Cited by 68 (1 self)
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A greedy approximation algorithm based on \spider decompositions " was developed by Klein and Ravi for node weighted Steiner trees. This algorithm provides a worst case approximation ratio of 2 ln k, where k is the number of terminals. However, the best known lower bound on the approximation ratio is ln k, assuming that NP 6 DT IM E[n O(log log n)], by a reduction from set cover [9, 4]. We show that for the unweighted case we can obtain an approximation factor of ln k. For the weighted case we develop a new decomposition theorem, and generalize the notion of \spiders " to \branchspiders", that are used to design a new algorithm with a worst case approximation factor of 1:5lnk. This algorithm, although polynomial, is not very practical due to its high running time; since we need to repeatedly nd many minimum weight matchings in each iteration. We are able to generalize the method to yield an approximation factor approaching 1:35 ln k. We also develop a simple greedy algorithm that is practical and has a worst case approximation factor of 1:6103 ln k. The techniques developed for the second algorithm imply a method of approximating node weighted network design problems de ned by 01 proper functions. These new ideas also lead to improved approximation guarantees for the problem of nding a minimum node weighted connected dominating set. The previous best approximation guarantee for this problem was 3 ln n [7]. By a direct application of the methods developed in this paper we are able to develop an algorithm with an approximation factor approaching 1:35 ln n. 1.
A SourceBased Algorithm For DelayConstrained MinimumCost Multicasting
, 1995
"... A new heuristic algorithm is presented for constructing minimumcost multicast trees with delay constraints. The new algorithm can set variable delay bounds on destinations and handles two variants of the network cost optimization goal: one minimizing the total cost (total bandwidth utilization) of ..."
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Cited by 54 (0 self)
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A new heuristic algorithm is presented for constructing minimumcost multicast trees with delay constraints. The new algorithm can set variable delay bounds on destinations and handles two variants of the network cost optimization goal: one minimizing the total cost (total bandwidth utilization) of the tree, and another minimizing the maximal link cost (the most congested link). Instead of the singlepass tree construction approach used in most previous heuristics, the new algorithm is based on a feasible search optimization method which starts with the minimumdelay tree and monotonically decreases the cost by iterative improvement of the delaybounded tree. The optimality of the costs of the delaybounded trees obtained with the new algorithm is analyzed by simulation. Depending on how tight the delay bounds are, the costs of the multicast trees obtained with the new algorithm are shown to be very close to the costs of the trees obtained by the Kou, Markowsky and Berman's algorithm. ...
An Iterative Algorithm for DelayConstrained MinimumCost Multicasting
 IEEE/ACM Transactions on Networking
, 1998
"... The bounded shortest multicast algorithm (BSMA) is presented for constructing minimumcost multicast trees with delay constraints. BSMA can handle asymmetric link characteristics and variable delay bounds on destinations, specified as real values, and minimizes the total cost of a multicast routing ..."
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Cited by 45 (1 self)
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The bounded shortest multicast algorithm (BSMA) is presented for constructing minimumcost multicast trees with delay constraints. BSMA can handle asymmetric link characteristics and variable delay bounds on destinations, specified as real values, and minimizes the total cost of a multicast routing tree. Instead of the singlepass tree construction approach used in most previous heuristics, the new algorithm is based on a feasiblesearch optimization strategy that starts with the minimumdelay multicast tree and monotonically decreases the cost by iterative improvement of the delaybounded multicast tree. BSMA's expected time complexity is analyzed, and simulation results are provided showing that BSMA can achieve nearoptimal cost reduction with fast execution.
Solving Steiner tree problems in graphs to optimality
 Networks
, 1998
"... Abstract: In this paper, we present the implementation of a branchandcut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms, and primal heuristics. We are able to ..."
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Cited by 44 (1 self)
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Abstract: In this paper, we present the implementation of a branchandcut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms, and primal heuristics. We are able to solve nearly all problem instances discussed in the literature to optimality, including one problem that—to our knowledge—has not yet been solved. We also report on our computational experiences with some very large Steiner tree problems arising from the design of electronic circuits. All test problems are gathered in a newly introduced library called SteinLib that is accessible via the World Wide Web. � 1998 John