1. Attack-Resistant Networks Allen G. Taylor agtaylor@ece.pdx.edu http://www.databasecentral.info/ Communication networks have four primary objectives: Minimize the delay of a signal traveling from any node to any other node Minimize cost Minimize degradation caused by random failures Minimize degradation caused by deliberate attacks These objectives conflict with each other, so a Pareto-optimal surface in four-dimensional space defines the set of solutions that are better than all other possible solutions. The best solution in any particular case will be a point on the surface that gives the best performance with respect to the highest-ranked objective, while still giving high performance to the second-ranked and following objectives. Can modified topology reduce the damage? Networks can be damaged in two basic ways, destroying hubs and destroying links. For most networks, destroying hubs is more damaging, since taking out a hub simultaneously takes out multiple links. The more highly connected a hub is, the more damaging its destruction would be. Reducing the degree of hubs and adding redundant hubs and links should improve network survivability. However, adding redundancy adds cost and reducing hub degree may impair performance. Paradoxically, reducing hub degree may also reduce resistance to random failures. Barabasi biased the attachment of subsequent nodes away from a pure random choice by giving nodes of higher degree a higher probability of being a destination of a new node. This “preferential attachment” strategy implements the “rich get richer” phenomenon, in which nodes that are already highly connected tend to attract new connections more readily than do nodes of lower degree. This procedure tends to produce networks with a few nodes of high degree, more nodes of medium degree, and many nodes of low degree--a scale-free distribution. I decided to examine a three-dimensional slice of the four- dimensional solution space, by fixing cost and generating a Pareto surface for the other three objectives. I fix cost for a network with a given number of nodes by mandating that each node have exactly two outgoing links. Thus for any given test case, there are a specified number of nodes and twice as many links. This results in a sparse network of moderate cost. I test the networks generated according to this constraint, using incremental node addition, but not using preferential attachment. The test consists of removing the most highly connected nodes from the network and assessing the effect of such damage on performance and on the loss of connectivity to undamaged nodes. After recording data on performance and network integrity on the test networks, I subject them to modification by recombination and mutation operations that evolve networks rather than the bit strings that would be modified by a genetic algorithm. The networks evolve toward a topology that is more resistant to deliberate attack than the original networks, but still retains high performance and resistance to random failure. After evolving optimal networks, I characterize them according to the degree distribution of their hubs and their clustering coefficients. This information can then be used as guidelines when designing real networks that must be resistant to deliberate attack as well as being resistant to random failure, low cost, and high performance. I am using an evolutionary computation approach to network design that simultaneously maximizes resistance to deliberate attack, resistance to random failure, and performance, while minimizing cost. Depending on the weights given to each of the four objectives, the optimal point will be located somewhere on a four-dimensional Pareto front of optimal solutions. Scale-free networks have been shown by Barabasi and his collaborators to be resistant to random failures, low cost, and high performance, but particularly vulnerable to deliberate attack. Barabasi constructed his test networks of some predetermined size by starting with two “seed” nodes and attaching a third node to one of the two, chosen at random. Selected Publications A. G. Taylor, A. Gibbs, "Automated Search for Lunar Lava Tubes in the Clementine Data Set", Workshop on New Views of the Moon: Integrated Remotely Sensed, Geophysical, and Sample Datasets, Sept. 18–20, 1998 Houston, Texas The next node is attached to one of the existing three, and so on. Because of the incremental nature of adding new nodes, older nodes tend to have higher degree than recently added nodes.