Exact Computation Of Graph Edit Distance For Uniform And Non-Uniform Metric Edit Costs

The graph edit distance is a well-established and widely used distance measure for labelled, undirected graphs. However, since its exact computation is NP-hard, research has mainly focused on devising approximative heuristics and only few exact algorithms have been proposed. The standard approach A(star)-GED, a node-based best-first search that works for both uniform and non-uniform metric edit costs, suffers from huge runtime and memory requirements. Recently, two better performing algorithms have been proposed: DF-GED, a node-based depth-first search that works for uniform and non-uniform metric edit costs, and CSI_GED, an edge-based depth-first search that works only for uniform edit costs. Our paper contains two contributions: First, we propose a speed-up DF-GED(u) of DF-GED for uniform edit costs. Second, we develop a generalisation CSI_GED(nu) of CSI_GED that also covers non-uniform metric edit cost. We empirically evaluate the proposed algorithms. The experiments show, i.a., that our speed-up DF-GED(u) clearly outperforms DF-GED and that our generalisation CSI_GED(nu) is the most versatile algorithm.