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.

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.

To provide real-time service or engineer constrained-based paths, networks require the underlying routing algorithm to be able to find low-cost paths that satisfy given Quality-of-Service (QoS) constraints. However, the problem of constrained...

With the proliferation of multimedia group applications, the construction of multicast trees satisfying Quality of Service (QoS) requirements is becoming a problem of prime importance. Many of the multicast applications (such as video broadcasts and teleconferencing) require the network to support dynamic multicast sessions wherein the membership of the multicast group changes with time. In this paper,

In this paper we propose a distributed protocol for constructing delay-bounded minimum-cost multicast trees in computer networks. The proposed protocol does not require knowledge of the complete network topology. Furthermore, it is unnecessary to know how many nodes are in the networks and which nodes are group members in advance. It is shown, through analysis and simulation on a class of random graphs, that our protocol only uses O(n) messages in the best case, where n is the number of nodes in the networks. Even in the worst case, our protocol uses O(d∗n) messages that has lower message complexity than previous protocols, where d is the average nodal degree.

To support real-time multimedia applications in BISDN networks, QoS guaranteed multicast routing is essential. Traditional multicast routing algorithms used for solving the Steiner tree problem cannot be used in this scenario, because QoS constraints on links are not considered. In this paper, we present two efficient source-based multicast routing algorithms in directed networks. The objective of the routing algorithms is to minimize the multicast tree cost while maintaining a bound on delay. Simulation results show that these two heuristics can greatly improve the multicast tree cost measure in comparison with the shortest path routing schemes. Their performance is close to that of the known CST � algorithm proposed by Kompell et al. in Reference 1, but requiring a much shorter computation time.

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, center-based 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.

The cost structures for resource allocation in many network design problems obey economies of scale, meaning that the cost per unit resource becomes cheaper as the amount of resources allocated increases. For instance, if we are purchasing cables to route data in a network, the cost per unit bandwidth reduces as the bandwidth we need to route increases. Another feature of resource allocation is granularity, meaning that the resource can only be purchased in multiples of a certain minimum quantity. Again, in the context of purchasing cables in a network, the minimum capacity cable available might be a T1 line with capacity 1 Mbps. In this

The problem of finding a minimum-cast multicast tree ( Steiner tree) is known as NP-complete. Heuristic-based algorithms for this problem to achieve good performance are usually time-consuming. In this paper, we propose a new strategy called tree-caching for efficient setup of multicast connections in connection-oriented networks. In this scheme, the tree topologies that have been computed are cached in a database of the source nodes and can be used for setup of subsequent connection requests which have some common multicast members. This can reduce the connection establishment time by an efficient reuse of cached trees without having to rerun a multicast routing algorithm for the whole group. This gain is obtained by eliminating, whenever possible, the expensive tree computation algorithm that has to be performed in setting up a multicast connection. We first formulate the problem of tree-caching. We then propose a tree-caching algorithm to reduce the complexity of the tree computations when a new connection is to be established. Through simulations, we find that the proposed treecaching strategy perform well and can significantly reduce the computation complexity for setting up multicast connections. Index terms---Multicast, caching, Delay-constraint A.

Abstract — Whereas multicast transmission in one-to-many communications allows the operator to drastically save network resources, it also makes the routing of the traffic flows more complex then in unicast transmissions. A huge amount of possible trees have to be considered and analyzed to find the appropriate routing paths. To address this problem, we propose the use of the genetic algorithms (GA), which considerably reduce the number of solutions to be evaluated. A heuristic procedure is first used to discern a set of possible trees for each multicast session in isolation. Then, the GA are applied to find the appropriate combination of the trees to comply with the bandwidth needs of the group of multicast sessions simultaneously. The goodness of each solution is assessed by means of an expression that weights both network bandwidth allocation and one-way delay. The resulting cost function is guided by few parameters that can be easily tuned during traffic engineering operations; an appropriate setting of these parameters allows the operator to configure the desired balance between network resource utilization and provided quality of service. Simulations have been performed to compare the proposed algorithm with alternative solutions in terms of bandwidth utilization and transmission delay. Index Terms — Group multicast routing; Multicast services; Genetic Algorithms.