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Distributed Algorithms for Multicast Path Setup in Data Networks
 IEEE/ACM Transactions on Networking
, 1995
"... Establishing a multicast tree in a pointtopoint network of switch nodes, such as a widearea ATM network, can be modeled as the NPcomplete Steiner problem in networks. In this paper, we introduce and evaluate two distributed algorithms for finding multicast trees in pointtopoint data networks. ..."
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Cited by 54 (2 self)
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Establishing a multicast tree in a pointtopoint network of switch nodes, such as a widearea ATM network, can be modeled as the NPcomplete Steiner problem in networks. In this paper, we introduce and evaluate two distributed algorithms for finding multicast trees in pointtopoint data networks. These algorithms are based on the centralized Steiner heuristics, the shortest path heuristic (SPH) and the Kruskalbased shortest path heuristic (KSPH), and have the advantage that only the multicast members and nodes in the neighborhood of the multicast tree need to participate in the execution of the algorithm. We compare our algorithms by simulation against a baseline algorithm, the pruned minimum spanningtree heuristic, which is the basis of many previously published algorithms for finding multicast trees. Our results show that the competitiveness (the ratio of the sum of the heuristic tree's edge weights to that of the best solution found) of both of our algorithms was on the average ...
A Survey of Combinatorial Optimization Problems in Multicast Routing
, 2003
"... In multicasting routing, the main objective is to send data from one or more source to multiple destinations, while at the same time minimizing the usage of resources. Examples of resources which can be minimized include bandwidth, time and connection costs. In this paper we survey applications of c ..."
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Cited by 40 (1 self)
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In multicasting routing, the main objective is to send data from one or more source to multiple destinations, while at the same time minimizing the usage of resources. Examples of resources which can be minimized include bandwidth, time and connection costs. In this paper we survey applications of combinatorial optimization to multicast routing. We discuss the most important problems considered in this area, as well as their models. Algorithms for each of the main problems are also presented.
A distributed algorithm of delaybounded multicast routing for multimedia applications in wide area networks
 IEEE/ACM Transactions on Networking Vol.6 No.6
, 1998
"... Abstract—Multicast routing is to find a tree which is rooted from a source node and contains all multicast destinations. There are two requirements of multicast routing in many multimedia applications: optimal network cost and bounded delay. The network cost of a tree is defined as the sum of the c ..."
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Cited by 37 (1 self)
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Abstract—Multicast routing is to find a tree which is rooted from a source node and contains all multicast destinations. There are two requirements of multicast routing in many multimedia applications: optimal network cost and bounded delay. The network cost of a tree is defined as the sum of the cost of all links in the tree. The bounded delay of a routing tree refers to the feature that the accumulated delay from the source to any destination along the tree shall not exceed a prespecified bound. This paper presents a distributed heuristic algorithm which generates routing trees having a suboptimal network cost under the delay bound constraint. The proposed algorithm is fully distributed, efficient in terms of the number of messages and convergence time, and flexible in dynamic membership changes. A large amount of simulations have been done to show the network cost of the routing trees generated by our algorithm is similar to, or even better than, other existing algorithms. Index Terms — Delaybounded multicast, distributed routing algorithm, multicast routing, multimedia systems, realtime communications. I.
Distributed Dual Ascent Algorithm for Steiner Problems in Networks
"... Abstract. Steiner Problems in undirected or directed graphs are often used to model multicast routing problems. The directed case being particularly suitable to situations where most of the trafic has a single source. Sequential Steiner heuristics are not convenient in that context, since one can no ..."
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Cited by 6 (0 self)
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Abstract. Steiner Problems in undirected or directed graphs are often used to model multicast routing problems. The directed case being particularly suitable to situations where most of the trafic has a single source. Sequential Steiner heuristics are not convenient in that context, since one can not assume that a central node has complete information about the topology and the state of a large wide area network. This work presents a distributed version of the Dual Ascent Heuristic proposed by Wong, known for its remarkable good practical results, lower and upper bounds, in both undirected and directed Steiner problems. The distributed Dual Ascent has worst case complexities of O(V  2) time and O(T .V  2) messages. Experimental results are also presented, showing the eficiency of the proposed algorithm. 1.
OPTIMIZATION PROBLEMS IN MULTICAST TREE CONSTRUCTION
"... ABSTRACT. Multicasting is a technique for data routing in networks that allows multiple destinations to be addressed simultaneously. The implementation of multicasting requires, however, the solution of difficult combinatorial optimization problems. In this chapter, we discuss combinatorial issues o ..."
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Cited by 6 (2 self)
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ABSTRACT. Multicasting is a technique for data routing in networks that allows multiple destinations to be addressed simultaneously. The implementation of multicasting requires, however, the solution of difficult combinatorial optimization problems. In this chapter, we discuss combinatorial issues occurring in the implementation of multicast routing, including multicast tree construction, minimization of the total message delay, centerbased routing, and multicast message packing. Optimization methods for these problems are discussed and the corresponding literature reviewed. Mathematical programming as well as graph models for these problems are discussed. 1.
Steiner Tree Based Distributed Multicast Routing in Networks
 STEINER TREES IN INDUSTRIES D.Z. DU AND X. CHENG (EDS.)
, 2000
"... ..."
Distributed DegreeConstrained Multicasting in PointtoPoint Networks
, 1995
"... Establishing a multicast tree in a pointtopoint network of switch nodes, such as a widearea ATM network, is often modeled as the NPcomplete Steiner problem in networks. In this paper, we present distributed algorithms for finding efficient multicast trees in the presence of constraints on the ..."
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Cited by 2 (0 self)
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Establishing a multicast tree in a pointtopoint network of switch nodes, such as a widearea ATM network, is often modeled as the NPcomplete Steiner problem in networks. In this paper, we present distributed algorithms for finding efficient multicast trees in the presence of constraints on the copying ability of the individual switch nodes in the network. We refer to this problem as the degreeconstrained multicast tree problem and model it as the degreeconstrained Steiner problem (DCSP) in networks. We consider two distinct approaches to the design of distributed DCPS heuristics. The first approach involves design of distributed versions of centralized DCSP algorithms. We introduce distributed versions of two DCSP heuristics: the shortest path heuristic (SPH) and the Kruskalbased shortest path heuristic (KSPH). The second approach is to modify the solution obtained from an unconstrained heuristic to satisfy the degree constraints using a distributed postprocessing algor...
A Superstabilizing log(n)Approximation Algorithm for Dynamic Steiner Trees
, 902
"... In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimumweight spanning tree a subset of nodes of a network (referred as Steiner members or Steiner group). Steiner trees are good candidates to efficiently ..."
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In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimumweight spanning tree a subset of nodes of a network (referred as Steiner members or Steiner group). Steiner trees are good candidates to efficiently implement communication primitives such as publish/subscribe or multicast, essential building blocks for the new emergent networks (e.g. P2P, sensor or adhoc networks). The cost of the solution returned by our algorithm is at most log S  times the cost of an optimal solution, where S is the group of members. Our algorithm improves over existing solutions in several ways. First, it tolerates the dynamism of both the group members and the network. Next, our algorithm is selfstabilizing, that is, it copes with nodes memory corruption. Last but not least, our algorithm is superstabilizing. That is, while converging to a correct configuration (i.e., a Steiner tree) after a modification of the network, it keeps offering the Steiner tree service during the stabilization time to all members that have not been affected by this modification. 1
PAPER Special Section on Concurrent/Hybrid Systems: Theory and Applications An Optimal Share Transfer Problem on Secret Sharing Storage Systems
, 2007
"... SUMMARY We have been developing a secure and reliable distributed storage system, which uses a secret sharing scheme. In order to efficiently store data in the system, this paper introduces an optimal share transfer problem, and proves it to be, generally, NPhard. It is also shown that the problem ..."
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SUMMARY We have been developing a secure and reliable distributed storage system, which uses a secret sharing scheme. In order to efficiently store data in the system, this paper introduces an optimal share transfer problem, and proves it to be, generally, NPhard. It is also shown that the problem can be resolved into a Steiner tree problem. Finally, through computational experiments we perform the comparison of heuristic algorithms for the Steiner tree problem. key words: distributed storage system, secret sharing scheme, Steiner tree, NPcomplete, distributed algorithm 1.