A binary linear programming formulation of the graph edit distance for unweighted, undirected graphs with vertex attributes is derived and applied to a graph recognition problem. A general formulation for editing graphs is used to derive a graph edit distance that is proven to be a metric, provided the cost function for individual edit operations is a metric. Then, a binary linear program is developed for computing this graph edit distance, and polynomial time methods for determining upper and lower bounds on the solution of the binary program are derived by applying solution methods for standard linear programming and the assignment problem. A recognition problem of comparing a sample input graph to a database of known prototype graphs in the context of a chemical information system is presented as an application of the new method. The costs associated with various edit operations are chosen by using a minimum normalized variance criterion applied to pairwise distances between nearest neighbors in the database of prototypes. The new metric is shown to perform quite well in comparison to existing metrics when applied to a database of chemical graphs.

We consider the problem of estimating the endpoints (source and destination) of a transmission in a network based on partial measurement of the transmission path. Possibly asynchronous sensors placed at various points within the network provide the basis for endpoint estimation by indicating that a specific transmission has been intercepted at their assigned locations. During a training phase, test transmissions are made between various pairs of endpoints in the network and the sensors they activate are noted. Sensor activations corresponding to transmissions with unknown endpoints are also observed in a monitoring phase. A semidefinite programming relaxation is used in conjunction with the measurements and linear prior information to produce likely sample topologies given the data. These samples are used to generate Monte Carlo approximations of the posterior distributions of source/destination pairs for measurements obtained in the monitoring phase. The posteriors allow for maximum a posteriori (MAP) estimation of the endpoints along with computation of some resolution measures. We illustrate the method using simulations of random topologies