A new heuristic algorithm is presented for constructing minimum-cost 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 single-pass 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 delay-bounded tree. The optimality of the costs of the delay-bounded 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. ...

Abstract We present the Cost-Distance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of source-sink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for Cost-Distance, 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 single-sink buy-at-bulk with variable pipe types between different sets of nodes, facility location with buy-at-bulk 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 constant-approximations 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 buy-at-bulk 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 Cost-Distance 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.

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The bounded shortest multicast algorithm (BSMA) is presented for constructing minimum-cost 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 single-pass tree construction approach used in most previous heuristics, the new algorithm is based on a feasiblesearch optimization strategy that starts with the minimum-delay multicast tree and monotonically decreases the cost by iterative improvement of the delay-bounded multicast tree. BSMA's expected time complexity is analyzed, and simulation results are provided showing that BSMA can achieve near-optimal cost reduction with fast execution.

Establishing a multicast tree in a point-to-point network of switch nodes, such as a wide-area ATM network, can be modeled as the NP-complete Steiner problem in networks. In this paper, we introduce and evaluate two distributed algorithms for finding multicast trees in point-to-point data networks. These algorithms are based on the centralized Steiner heuristics, the shortest path heuristic (SPH) and the Kruskalbased shortest path heuristic (K-SPH), 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 spanning-tree 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 ...

Establishing a multicast tree in a point-to-point network of switch nodes, such as a wide-area ATM network, is often modeled as the NP-complete Steiner problem in networks. In this paper, we study 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 degree-constrained multicast tree problem and model it as the degree-constrained Steiner problem in networks. Steiner heuristics for the degree-constrained case are proposed and their simulation results for sparse, point-to-point networks are presented. The results are compared with respect to their quality of solution, cost (running time), and the number of test cases for which no solution could be found. The results of our research indicate that efficient multicast trees can be found in large, sparse networks with small multicast groups even with limited multicast capability in the individual switches. Some of ...

We give a simple algorithm to find a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the two trees and a fl? 0, the algorithm returns a spanning tree in which the distance between any vertex and the root of the shortest-path tree is at most 1 + p 2fl times the shortest-path distance, and yet the total weight of the tree is at most 1 + p 2=fl times the weight of a minimum spanning tree. Our algorithm runs in linear time and obtains the best-possible trade-off. It can be implemented on a CREW PRAM to run in logarithmic time using one processor per vertex.

All-optical WDM networks are fast becoming the natural choice for future backbone. In this paper, we establish the efficiency of multicasting over unicasting in all-optical WDM networks, assess the usefulness of wavelength conversion for multicasting, and explore the issues related to the splitting (or copying) capability of the nodes. The comparison between multicasting and unicasting is based on the number of wavelengths as well as the amount of bandwidth required for a given set of multicasting sessions. For each multicasting session, a source-specific multicasting forest (or trees) is constructed first, taking into account the sparse splitting capability of the nodes in the network. Then, each multicasting tree is partitioned into segments according to the sparse wavelength conversion capability of the nodes on the tree such that each segment needs to be assigned the same wavelength. Simulation results obtained for a practical network such as NSFNET and randomly generated networks ...

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.

We propose a combined multicast routing and resource reservation protocol, termed Reservation-Based Multicast (RBM), that performs routing in a fashion similar to Protocol Independent Multicast (PIM), but which is intended for mobile operation and routes hierarchically-encoded data streams based on user-specified fidelity requirements, real-time delivery thresholds and prevailing network bandwidth constraints. The protocol retains the fully distributed operation, scalability and receiver-initiated orientation of PIM; but, unlike PIM, the protocol is tightly coupled to an underlying, distributed, unicast routing protocol thereby facilitating operation in a dynamic topology. This paper focuses on the initial route construction phase, assumed to occur during a static "snapshot" of the dynamic topology, and is therefore applicable to fixed networks as well, e.g. the Internet. A forthcoming paper will detail the protocol's robustness and adaptivity to arbitrary topological changes during bot...