Exact and Heuristic Algorithms for Solving the Generalized Minimum Filter Placement Problem

by Mofya, Enock Chisonge.

We consider a problem of placing route-based filters in a communication network to limit the number of forged address attacks to a prescribed level. Nodes in the network communicate by exchanging packets along arcs, and the originating node embeds the origin and destination addresses within each packet that it sends. In the absence of a validation mechanism, one node can send packets to another node using a forged origin address to launch an attack against that node. Route-based filters can be established at various nodes on the communication network to protect against these attacks. A route-based filter examines each packet arriving at a node, and determines whether or not the origin address could be legitimate, based on the arc on which the packet arrives, the routing information, and possibly the destination. The problem we consider seeks to find a minimum cardinality subset of nodes to filter so that the prescribed level of security is achieved. The primary contributions of this dissertation are as follows. We formulate and discuss the modeling of this filter placement problem as a mixed-integer program. We then show the sensitivity of the optimal number of deployed filters as the required level of security changes, and demonstrate that current vertex cover-based heuristics are ineffective for problems with relaxed security levels. We identify a set of special network topologies on which the filter placement problem is solvable in polynomial time, focusing our attention on the development of a dynamic programming algorithm for solving this problem on tree networks. These results can then in turn be used to derive valid inequalities for a mixed-integer programming model of the filter placement problem. Finally, we present heuristic algorithms based on the insights gained from our overall study for solving the problem, and evaluate their performance against the optimal solution provided by our mixed-integer programming model. 11