Comparing Stars: On Approximating Graph Edit Distance

  title={Comparing Stars: On Approximating Graph Edit Distance},
  author={Zhiping Zeng and Anthony K. H. Tung and Jianyong Wang and Jianhua Feng and Lizhu Zhou},
  journal={Proc. VLDB Endow.},
Graph data have become ubiquitous and manipulating them based on similarity is essential for many applications. Graph edit distance is one of the most widely accepted measures to determine similarities between graphs and has extensive applications in the fields of pattern recognition, computer vision etc. Unfortunately, the problem of graph edit distance computation is NP-Hard in general. Accordingly, in this paper we introduce three novel methods to compute the upper and lower bounds for the… 

Figures and Tables from this paper

Measuring Similarity between Graphs Based on the Levenshtein Distance

This work turned the graph matching problem into string matching, which gains great improvement on the matching performance, and proposed a novel method for similarity measurement of graphs.

Efficient Parallel Computing of Graph Edit Distance

This paper proposes a novel efficient parallel algorithm based on the state-of-the-art GED algorithm AStar+-LSa, called PGED, which is to allocate the heavy workload of searching the optimal vertex mapping between two graphs to multiple threads based on an effective allocation strategy, resulting in high efficiency of GED computation.

Convex graph invariant relaxations for graph edit distance

This paper proposes a new family of computationally tractable convex relaxations for obtaining lower bounds on graph edit distance and proves under suitable conditions that these relaxations are tight when one of the graphs consists of few eigenvalues.

Improved local search for graph edit distance

BFST_ED: A Novel Upper Bound Computation Framework for the Graph Edit Distance

A novel upper bound computation framework for the graph edit distance that combines vertex map construction with edit counting in an easy and straightforward manner and allows to compare graphs from different hierarchical views to improve the upper bound.

A Quadratic Assignment Formulation of the Graph Edit Distance

The proposed approach is generally able to reach a more accurate approximation of the optimal GED than the bipartite GED, with a computational cost that is still affordable for graphs of non trivial sizes.

Speeding Up Graph Edit Distance Computation with a Bipartite Heuristic

The idea is to use a fast but suboptimal bipartite graph matching algorithm as a heuristic function that estimates the future costs so that it is guaranteed to return the exact graph edit distance of two given graphs.

Fast Suboptimal Algorithms for the Computation of Graph Edit Distance

This paper proposes two simple, but effective modifications of a standard edit distance algorithm that allow us to suboptimally compute edit distance in a faster way and demonstrates the resulting speedup and shows that classification accuracy is mostly not affected.

A binary linear programming formulation of the graph edit distance

  • D. JusticeA. Hero
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 2006
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, and the new metric is shown to perform quite well in comparison to existing metrics when applications to a database of chemical graphs.

SAGA: a subgraph matching tool for biological graphs

SAGA employs a flexible model for computing graph similarity, which allows for node gaps, node mismatches and graph structural differences, and is orders of magnitude faster than existing methods.

A graph distance metric based on the maximal common subgraph

Similarity evaluation on tree-structured data

This paper proposes to transform tree-structured data into an approximate numerical multidimensional vector which encodes the original structure information and proves that the L1 distance of the corresponding vectors, whose computational complexity is O(|T1| + |T2|), forms a lower bound for the edit distance between trees.

Graph Indexing: Tree + Delta >= Graph

This study verifies that (Tree+Δ) is a better choice than graph for indexing purpose, denoted (Tree-Δ ≥Graph), to address the graph containment query problem and achieves an order of magnitude better performance in index construction.

Feature-based similarity search in graph structures

This article investigates the issues of substructure similarity search using indexed features in graph databases and proves that the complexity of optimal feature set selection is Ω(2m) in the worst case, where m is the number of features for selection.

Closure-Tree: An Index Structure for Graph Queries

The concept of a graph closure, a generalized graph that represents a number of graphs, is introduced and the indexing technique, called Closure-tree, organizes graphs hierarchically where each node summarizes its descendants by a graphclosure.

Graph indexing: a frequent structure-based approach

The gIndex approach not only provides and elegant solution to the graph indexing problem, but also demonstrates how database indexing and query processing can benefit form data mining, especially frequent pattern mining.