Multicast under Constraints in Coalition and Command-and-Control Networks Prithwish Basu Raytheon BBN Technologies Cambridge, MA pbasu@bbn.com Chi-Kin Chau University of Cambridge Cambridge UK ckc25@cam.ac.uk Saikat Guha Raytheon BBN Technologies Cambridge, MA sguha@bbn.com Richard Gibbens University of Cambridge Cambridge UK richard.gibbens@cl.cam.ac.uk Abstract—Multicast has been well-studied in the networking literature in both wired and wireless network contexts in the last several decades. However, multicast routing under physical or logical communication constraints has not received much atten- tion. Such communication constraints are imposed in scenarios such as coalition networks where two teams are participating in a joint operation, or command-and-control (C 2 ) networks where the flow of control obeys hierarchical relationship regardless of the physical connectivity between the communication devices. In this paper, we first consider the problem of multicast routing in coalition network environments where nodes can talk across coalition boundaries via “gateway” routers. The goal here is to find a minimum cost node-weighted Steiner tree with a novel twist that the node costs are not purely additive – in fact, the overall cost to multicast to the specified sink nodes depends on how many times the gateway nodes had to perform the “gatewaying operation”. We show how one can transform (or augment) an input network graph with non-additive costs to another one with additive costs. We then show how existing approximation algorithms for computing Steiner trees can be executed on the augmented graph and still achieve the O(log n) approximation guarantee. We study by thorough simulations the impact of the size and structure of the graph as well as the spatial distribution of coalition nodes and the weights on them on the overall cost of the multicast tree. We also investigate the multicasting problem under constraints imposed by the C 2 hierarchy, and give optimal and approximation algorithms for this problem. I. I NTRODUCTION The primary problem of multicast routing is to optimize the pathways of distribution of messages from one node to a given subset of nodes in any given network. Multicast routing has been studied in depth in the networking literature in both wired [3], [2] and wireless ad hoc network contexts [10], [12] in the last two decades. It has also been studied in the context of overlay networks [14]. While most of the approaches construct a tree spanning the terminal nodes, some approaches for wireless ad hoc network are mesh-based for reliability [12]. This research was sponsored by the U.S. Army Research Laboratory and the U.K. Ministry of Defense and was accomplished under Agreement Number W911NF-06-3-0002.l. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Army Research Laboratory, the U.S. Government, the U.K. Ministry of Defence or the U.K. Government. The U.S. and U.K. Governments are authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon. However, multicast routing under physical or logical com- munication constraints has not received much attention. Such communication constraints are imposed in scenarios such as coalition networks where two teams are participating in a joint operation, or command-and-control (C 2 ) networks where the flow of control obeys hierarchical relationship regardless of the physical connectivity between the communication devices. In this paper, we are interested in optimal (lowest cost) multicast to a specified set of receivers while obeying physical or logical constraints. Physical constraints may be imposed by the fact that two nearby nodes (say, one from US and another from UK) that may be sharing the same communication frequency may not always be able to communicate if they do not share a common link-layer encryption key. A third node that is a neighbor of both the aforementioned nodes could instead serve as a “gateway” for translating messages between the two parties in the coalition [1]. In such a setting, however, the cost of multicast is a function of the number of times a message is being translated between the coalition parties. This results in the total cost of multicast being not necessarily additive and thus existing approaches for multicast tree construction may not directly apply to this scenario. In this paper, we show how one can transform (or augment) an input network graph with non-additive costs stemming from message translation described above to another graph with additive costs. We then show how existing approximation algorithms for computing Steiner trees can be executed on the augmented graph and still achieve the O(log n) approximation guarantee. In the second part of the paper, we study the multicast routing problem in the presence of logical constraints such as those imposed by the Command and Control (or C 2 ) hierarchy. Here, one node may be able to receive and route a message from its neighbor but may only be able to “read” the message if it is received from its parent node in the C 2 hierarchy. We first show that the C 2 constraints may result in a piece of data traversing an edge multiple times, and that a multicast substructure (which is not necessarily a tree) that takes the constraints imposed by the C 2 topology into account could have a lower cost than one which ignores the constraints. Our contributions are as follows: • Optimization problem formulation of the gateway- assisted multicast problem with non-additive costs.