Graph Edit Distance – Optimal and Suboptimal Algorithms with Applications

Bunke, Horst; Riesen, Kaspar

doi:10.1002/9783527627981.ch6

Cited by 9 publications

(3 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is computed as a number of edit operations (add, delete, and swap in the case of a labeled graph) required to match two graphs [6], or, in a special case, trees [4]. The edit distance focuses on finding an isomorphism between graphs/subgraphs, while for merge trees we can have two isomorphic trees with a positive distance (see the example in Fig.…”

Section: Distance Between Graphsmentioning

confidence: 99%

See 1 more Smart Citation

Measuring the Distance Between Merge Trees

Beketayev

Yeliussizov

Morozov

et al. 2014

Mathematics and Visualization

View full text Add to dashboard Cite

Merge trees represent the topology of scalar functions. To assess the topological similarity of functions, one can compare their merge trees. To do so, one needs a notion of a distance between merge trees, which we define. We provide examples of using our merge tree distance and compare this new measure to other ways used to characterize topological similarity (bottleneck distance for persistence diagrams) and numerical difference (L ∞ -norm of the difference between functions).

show abstract

Section: Distance Between Graphsmentioning

confidence: 99%

“…We generate three bivariate (or 2D) functions f 1 , f 2 , f 3 , and three trivariate (or 3D) functions f 4 , f 5 , f 6 . We set the number of maxima to five, to keep them simple for visual exploration; see Fig.…”

Section: Analytical Functionsmentioning

confidence: 99%

Measuring the Distance Between Merge Trees

Beketayev

Yeliussizov

Morozov

et al. 2014

Mathematics and Visualization

View full text Add to dashboard Cite

show abstract

“…On graphs, the first edit distance to be considered is an analogue to the Levenshtein distance; insertion and deletion of vertices and edges are allowed, along with vertex and edge label substitution [22]. Graph edit distances have become an important tool in pattern recognition, which is at the heart of modern image processing and computer vision [5,12].…”

Section: Introductionmentioning

confidence: 99%

A framework for cost-constrained genome rearrangement under Double Cut and Join

Simonaitis,

Chateau,

Swenson

2018

Preprint

View full text Add to dashboard Cite

The study of genome rearrangement has many flavours, but they all are somehow tied to edit distances on variations of a multi-graph called the breakpoint graph. We study a weighted 2-break distance on Eulerian 2-edge-colored multi-graphs, which generalizes weighted versions of several Double Cut and Join problems, including those on genomes with unequal gene content. We affirm the connection between cycle decompositions and edit scenarios first discovered with the Sorting By Reversals problem. Using this we show that the problem of finding a parsimonious scenario of minimum cost on an Eulerian 2-edge-colored multi-graph -with a general cost function for 2-breaks -can be solved by decomposing the problem into independent instances on simple alternating cycles. For breakpoint graphs, and a more constrained cost function, based on coloring the vertices, we give a polynomial-time algorithm for finding a parsimonious 2-break scenario of minimum cost, while showing that finding a non-parsimonious 2-break scenario of minimum cost is NP-Hard.

show abstract