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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.
Biconnectivity Approximations and Graph Carvings
, 1994
"... A spanning tree in a graph is the smallest connected spanning subgraph. Given a graph, how does one find the smallest (i.e., least number of edges) 2connected spanning subgraph (connectivity refers to both edge and vertex connectivity, if not specified) ? Unfortunately, the problem is known to be ..."
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Cited by 84 (3 self)
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A spanning tree in a graph is the smallest connected spanning subgraph. Given a graph, how does one find the smallest (i.e., least number of edges) 2connected spanning subgraph (connectivity refers to both edge and vertex connectivity, if not specified) ? Unfortunately, the problem is known to be NP hard. We consider the problem of finding a better approximation to the smallest 2connected subgraph, by an efficient algorithm. For 2edge connectivity our algorithm guarantees a solution that is no more than 3 2 times the optimal. For 2vertex connectivity our algorithm guarantees a solution that is no more than 5 3 times the optimal. The previous best approximation factor is 2 for each of these problems. The new algorithms (and their analyses) depend upon a structure called a carving of a graph, which is of independent interest. We show that approximating the optimal solution to within an additive constant is NP hard as well. We also consider the case where the graph has edge weigh...
Evaluation of multicast routing algorithms for realtime communication on highspeed networks
 IEEE Journal on Selected Areas in Communications
, 1997
"... Multicast (MC) routing algorithms capable of satisfying the quality of service (QoS) requirements of realtime applications will be essential for future highspeed networks. We compare the performance of all of the important MC routing algorithms when applied to networks with asymmetric link loads. ..."
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Cited by 78 (4 self)
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Multicast (MC) routing algorithms capable of satisfying the quality of service (QoS) requirements of realtime applications will be essential for future highspeed networks. We compare the performance of all of the important MC routing algorithms when applied to networks with asymmetric link loads. Each algorithm is judged based on the quality of the MC trees it generates and its efficiency in managing the network resources. Simulation results over random networks show that unconstrained algorithms are not capable of fulfilling the QoS requirements of realtime applications in widearea networks. Simulations also reveal that one of the unconstrained algorithms, reverse path multicasting (RPM), is quite inefficient when applied to asymmetric networks. We study how combining routing with resource reservation and admission control improves RPM’s efficiency in managing the network resources. The performance of one semiconstrained heuristic, MSC, three constrained Steiner tree (CST) heuristics, KPP, CAO, and BSMA, and one constrained shortest path tree (CSPT) heuristic, CDKS are also studied. Simulations show that the semiconstrained and constrained heuristics are capable of successfully constructing MC trees which satisfy the QoS requirements of realtime traffic. However, the cost performance of the heuristics varies. BSMA’s MC trees are lower in cost than all other constrained heuristics. Finally, we compare the execution times of all algorithms, unconstrained, semiconstrained, and constrained.
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 ...
Multicast Routing with EndtoEnd Delay and Delay Variation Constraints
 IEEE Journal on Selected Areas in Communications
, 1995
"... We study the problem of constructing multicast trees to meet the quality of service requirements of realtime, interactive applications operating in highspeed packetswitched environments. In particular, we assume that multicast communication depends on (a) bounded delay along the paths from the so ..."
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Cited by 70 (2 self)
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We study the problem of constructing multicast trees to meet the quality of service requirements of realtime, interactive applications operating in highspeed packetswitched environments. In particular, we assume that multicast communication depends on (a) bounded delay along the paths from the source to each destination, and (b) bounded variation among the delays along these paths. We first establish that the problem of determining such a constrained tree is NPcomplete. We then derive heuristics that demonstrate good average case behavior in terms of the maximum interdestination delay variation of the final tree. In addition, our heuristics achieve their best performance under conditions typical of multicast scenarios in highspeed networks. We also show that it is possible to dynamically reorganize the initial tree in response to changes in the destination set, in a way that is minimally disruptive to the multicast session. Department of Computer Science North Carolina State Uni...
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.
Multicast Routing and Its QoS Extension: Problems, Algorithms, and Protocols
 IEEE Network
, 2000
"... Multicast services have been increasingly used in large scale continuous media applications. The qualityofservice (QoS) requirements of these continuous media applications prompt the necessity for QoSdriven, constraintbased multicast routing. This article provides a comprehensive overview of exi ..."
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Cited by 64 (0 self)
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Multicast services have been increasingly used in large scale continuous media applications. The qualityofservice (QoS) requirements of these continuous media applications prompt the necessity for QoSdriven, constraintbased multicast routing. This article provides a comprehensive overview of existing multicast routing algorithms, protocols, and their QoS extension. In particular, we classify multicast routing problems according to their optimization functions and performance constraints, present basic routing algorithms in each problem class, and discuss their strengths and weakness. We also categorize existing multicast routing protocols, outline the issues and challenges in providing QoS in multicast routing, and point out possible future research directions.
CostDistance: Two Metric Network Design
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the numbe ..."
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Cited by 61 (7 self)
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Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the number of sources. We reduce many common network design problems to CostDistance, obtaining (in some cases) the first known logarithmic approximation for them. These problems include singlesink buyatbulk with variable pipe types between different sets of nodes, facility location with buyatbulk type costs on edges, and maybecast with combind cost and distance metrics. Our algorithm is also the algorithm of choice for several previous network design problems, due to its ease of implementation and fast running time. 1 Introduction Consider designing a network from the ground up. We are given a set of customers, and need to place various servers and network links in order to cheaply provide sufficient service. If we only need to place the servers, this becomes the facility location problem and constantapproximations are known. If a single server handles all customers, and we impose the additional constraint that the set of available network link types is the same for every pair of nodes (subject to constant scaling factors on cost) then this is the single sink buyatbulk problem. We give the first known approximation for the general version of this problem with both servers and network links. We reduce the network design problem to an elegant theoretical framework: the CostDistance problem. We are given a graph with a single distinguished sink node (server). Every edge in this graph can be measured along two metrics; the first will be called cost and the second will be length. Note that the two metrics are entirely independent, and that there may be any number of parallel edges in the graph. We are given a set of sources (customers). Our objective is to construct a Steiner tree connecting the sources to the sink while minimizing the combined sum of the cost of the edges in the tree and sum over sources of the weighted length from source to sink.
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. ...