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. ...

In this paper, we propose and evaluate ARIES, a heuristic for updating multicast trees dynamically in large point-to-point networks. The algorithm is based on monitoring the accumulated damage to the multicast tree within local regions of the tree as nodes are added and deleted, and triggering a rearrangement when the number of changes within a connected subtree crosses a set threshold. We derive an analytical upper-bound on the competitiveness of the algorithm. We also present simulation results to compare the average-case performance of the algorithm with two other known algorithms for the dynamic multicast problem, GREEDY and EBA (Edge-Bounded Algorithm). Our results show that ARIES provides the best balance among competitiveness, computational effort, and changes in the multicast tree after each update. Keywords: multicast algorithms, on-line Steiner problem, rearrangeable multicast algorithms. 1 Introduction Many future applications of computer networks such as distance educati...

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 ...

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 ...

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 ...

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...

This paper deals with the problem of constructing Steiner trees of minimum weight with diameter bounded by d, spanning a given set of k vertices in a graph. Exact solutions or logarithmic ratio approximation algorithms were known before for the cases of d <= 5. Here we give a polynomial time approximation algorithm of ratio O(log k) for constant d, which is asymptotically optimal unless P = NP , and an algorithm of ratio O( k^{\epsilon})), for any fixed 0 < \epsilon < 1, for general d. Keywords: NP-hard problems, approximation algorithms, Steiner trees 1 Introduction 1.1 The problem This paper considers the problem of finding low diameter Steiner trees of minimum weight. Given an n-vertex graph G(V

Abstract—The delivery of quality video service often requires high bandwidth with low delay or cost in network transmission. Current routing protocols such as those used in the Internet are mainly based on the single-path approach (e.g., the shortest-path routing). This approach cannot meet the end-to-end bandwidth requirement when the video is streamed over bandwidth-limited networks. In order to overcome this limitation, we propose multipath routing, where the video takes multiple paths to reach its destination(s), thereby increasing the aggregate throughput. We consider both unicast (point-to-point) and multicast scenarios. For unicast, we present an efficient multipath heuristic (of complexity 3)), which achieves high bandwidth with low delay. Given a set of path lengths, we then present and prove a simple data scheduling algorithm as implemented at the server, which achieves the theoretical minimum end-to-end delay. For a network with unitcapacity links, the algorithm, when combined with disjoint-path routing, offers an exact and efficient solution to meet a bandwidth requirement with minimum delay. For multicast, we study the construction of multiple trees for layered video to satisfy the user bandwidth requirements. We propose two efficient heuristics on how such trees can be constructed so as to minimize the cost of their aggregation subject to a delay constraint. Index Terms—Bandwidth-delay constraints, multicast routing, multipath routing, quality-of-service (QoS) routing, video scheduling. I.