DeepAI AI Chat
Log In Sign Up

Computing Optimal Assignments in Linear Time for Graph Matching

by   Nils M. Kriege, et al.

Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the assignment problem typically requires cubic time and its pairwise computation is expensive on large datasets. In this paper, we develop an algorithm which can find an optimal assignment in linear time when the cost function between objects is represented by a tree distance. We employ the method to approximate the edit distance between two graphs by matching their vertices in linear time. To this end, we propose two tree distances, the first of which reflects discrete and structural differences between vertices, and the second of which can be used to compare continuous labels. We verify the effectiveness and efficiency of our methods using synthetic and real-world datasets.


page 1

page 2

page 3

page 4


Eccentricity function in distance-hereditary graphs

A graph G = (V,E) is distance hereditary if every induced path of G is a...

Many-to-Many Graph Matching: a Continuous Relaxation Approach

Graphs provide an efficient tool for object representation in various co...

On the computational complexity of the Steiner k-eccentricity

The Steiner k-eccentricity of a vertex v of a graph G is the maximum Ste...

EmbAssi: Embedding Assignment Costs for Similarity Search in Large Graph Databases

The graph edit distance is an intuitive measure to quantify the dissimil...

On adaptive algorithms for maximum matching

In the fundamental Maximum Matching problem the task is to find a maximu...

Optimal Algorithm to Reconstruct a Tree from a Subtree Distance

This paper addresses the problem of finding a representation of a subtre...

Towards Capacity-Aware Broker Matching: From Recommendation to Assignment

Online real estate platforms are gaining increasing popularity, where a ...