Speeding up Fast Bipartite Graph Matching Through a New Cost Matrix

Abstract

Bipartite (BP) has been seen to be a fast and accurate suboptimal algorithm to solve the Error-Tolerant Graph Matching problem. Recently, Fast Bipartite (FBP) has been presented that obtains the same distance value and node labelings but in a reduced time. Both algorithms approximate the quadratic problem in a linear problem and they do it through a speci¯c cost matrix. FBP imposes the Edit costs to be de¯ned such as the Edit distance is a distance function. Originally, the Hungarian method was used but it has been seen the Jonker-Volgenant linear solver obtains similar results than the Hungarian method but with an important run time reduction. Nevertheless, this second solver has some convergence problems on some speci¯c cost matrices. The aim of this paper is to de¯ne a new cost matrix such that the Jonker-Volgenant solver converges and the matching algorithm obtains the same distance value than the BP algorithm.

Learning graph-matching edit-costs based on the optimality of the oracle's node correspondences

“…In both datasets and all the experiments, we used the fast bipartite [20,41] as the graph-matching algorithm with different combinations of costs K v and K e . Moreover, the node substitution cost, C vs , is the Normalized Euclidean distance between node attributes, C vs ∈ [0, 1].…”

Approximating Graph Edit Distance Using GNCCP

“…The edit path γ corresponds to an optimal edit path. GED has been widely used by the structural pattern recognition community [15,4,11,12] despite the fact that such distance comes along with several drawbacks. First of all, computing the GED of two graphs requires to find a path having a minimal cost among all possible paths, which is a NP-complete problem [8].…”

Graph Edit Distance: Moving from global to local structure to solve the graph-matching problem

“…Fast Bipartite algorithm (FBP) [8] and Square Fast Bipartite algorithm (SFBP) [9] are two efficient algorithms to Edit Distance computation for general graphs that in a first step generates a matrix costs and in a second step, applies an optimal linear sum assignment algorithm on this matrix, similar to Bipartite Bipartite algorithm (BP) [10] but with a different cost matrix. The computational cost of BP is (( + ) 3 ) ( and are the number of nodes of both graphs) while the computational cost of FBP and SFBP is ((max ( , )) 3 ).…”

“…In the next section, we define attributed graphs and GED. In section three, we summarise SFBP [9]. In section four, we present eight local sub-structures and distances between them.…”