2006 ABinaryLinProgFormulofGED

• (Justice & Hero, 2006) ⇒ Derek Justice, Alfred Hero. (2006). “A Binary Linear Programming Formulation of the Graph Edit Distance.” In: IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(8). doi:10.1109/TPAMI.2006.152

Subject Headings: Graph Edit Distance Function.

Quotes

Index Terms

• Graph algorithms, Similarity measures, Structural Pattern Recognition, Graphs and Networks, Linear Programming, Continuation (homotopy) method

Abstract

• 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,

	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2006 ABinaryLinProgFormulofGED	Derek Justice Alfred Hero			A Binary Linear Programming Formulation of the Graph Edit Distance			http://www.eecs.umich.edu/~hero/Preprints/gedPAMI2 final.pdf	10.1109/TPAMI.2006.152