We present heuristics for multicast tree construction for communication that depends on: i) bounded end-to-end 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 NP-complete. We show that the heuristics demonstrate good average case behavior in terms of cost, as determined through simulations on a large number of graphs.

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 OR-Library, 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.

We give the first approximation algorithm for the node-weighted 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.

We study the problem of constructing multicast trees to meet the quality of service requirements of real-time, interactive applications operating in high-speed packet-switched 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 NP-complete. We then derive heuristics that demonstrate good average case behavior in terms of the maximum inter-destination delay variation of the final tree. In addition, our heuristics achieve their best performance under conditions typical of multicast scenarios in high-speed 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...

We investigate multicast routing for high-bandwidth delay-sensitive applications in a point-to-point network as an optimization problem. We associate an edge cost and an edge delay with each edge in the network. The problem is to construct a tree spanning the destina-tion nodes, such that it has the least cost, and so that the delay on the path from source to each destination is bounded. Since the problem is computationally in-tractable, we present an efficient approximation algo-rithm. Experimental results through simulations show that the performance of the heuristic is near optimal. I.

This dissertation examines the geometric Steiner tree problem: given a set of terminals in the plane, find a minimum-length interconnection of those terminals according to some geometric distance metric. In the process, however, it addresses a much more general and widely applicable problem, that of finding a minimum-weight spanning tree in a hypergraph. The geometric Steiner tree problem is known to be NP-complete for the rectilinear metric, and NP-hard for the Euclidean metric. The fastest exact algorithms (in practice) for these problems use two phases: First a small but sufficient set of full Steiner trees (FSTs) is generated and then a Steiner minimal tree is constructed from this set. These phases are called FST generation and FST concatenation, respectively, and an overview of each phase is presented. FST concatenation is almost always the most expensive phase, and has traditionally been accomplished via simple backtrack search or dynamic programming.

This paper addresses the problem of effective multicast tree construction for interactive audiovisual communication to several destinations. We believe that the effectiveness of a multicast tree for such applications is determined by two factors: (i) the end-to-end delay along the individual paths from source to each destination, and (ii) the cost of the multicast tree, for example, in terms of network bandwidth utilization. Note that while the cost of the tree should be minimized, it is sufficient simply to bound the delay. The problem of computing the optimal constrained multicast tree is NP-complete. We present two distributed algorithms that compute low cost trees with delay-bounded paths from the source to each destination. Keywords: Multicast, interactive multimedia, Steiner tree, distributed algorithm, constrained optimization. 1 Introduction Multicasting, the simultaneous transmission of data to multiple destinations, is now being viewed as a very important facility in netwo...

It has been widely recognized that physical layer impairments, including power losses, must be taken into account when routing optical connections in transparent networks. In this paper we study the problem of constructing light-trees under optical layer power budget constraints, with a focus on algorithms which can guarantee a certain level of quality for the signals received by the destination nodes. We define a new constrained light-tree routing problem by introducing a set of constraints on the source-destination paths to account for the power losses at the optical layer. We investigate a number of variants of this problem, we characterize their complexity, and we develop a suite of corresponding routing algorithms

The rectilinear Steiner tree problem is to find a minimum-length rectilinear interconnection of a set of points in the plane. A reduction from the rectilinear Steiner tree problem to the graph Steiner tree problem allows the use of exact algorithms for the graph Steiner tree problem to solve the rectilinear problem. Furthermore, anumber of more direct, geometric algorithms have been devised for computing optimal rectilinear Steiner trees. This paper surveys algorithms for computing optimal rectilinear Steiner trees and presents experimental results comparing nine of them: graph Steiner tree algorithms due to Beasley, Bern, Dreyfus and Wagner, Hakimi, and Shore, Foulds, and Gibbons and geometric algorithms due to Ganley and Cohoon, Salowe and Warme, and Thomborson, Alpern, and Carter. 1 Introduction The rectilinear Steiner tree (RST) problem is stated as follows: given a set T of n points called terminals in the plane, find a set S of additional points called Steiner points such tha...

This dissertation examines a number of geometric interconnection, partitioning, and placement problems arising in the field of VLSI physical design automation. In particular, many of the results concern the geometric Steiner tree problem: given a set of terminals in the plane, find a minimum-length interconnection of those terminals according to some geometric distance metric. Two new algorithms are introduced that compute optimal rectilinear Steiner trees. Both are provably faster than any previous algorithm for instances small enough to solve in practice, and both are also fast in practice. The first algorithm is a dynamic programming algorithm based on decomposing a rectilinear Steiner tree into full trees. A full tree is a Steiner tree in which every terminal is a leaf. Its time complexity is O(n3^n), where n is the number of terminals. The second algorithm modifies the first by the use of full-set screening, which is a process by which some candidate full trees are eliminated f...