On the Relation Between the Common Labelling and the Median Graph
This work addresses a foundational gap in graph-based pattern recognition, providing theoretical insights that could improve median graph computation methods.
The paper formally analyzes the relationship between the Common Labelling and Generalized Median Graph problems in structural pattern recognition, proving that the cost of common labelling upper-bounds the median cost and showing equivalence in some cases.
In structural pattern recognition, given a set of graphs, the computation of a Generalized Median Graph is a well known problem. Some methods approach the problem by assuming a relation between the Generalized Median Graph and the Common Labelling problem. However, this relation has still not been formally proved. In this paper, we analyse such relation between both problems. The main result proves that the cost of the common labelling upper-bounds the cost of the median with respect to the given set. In addition, we show that the two problems are equivalent in some cases.