# Generalized Median Graph via Iterative Alternate Minimizations

## TL;DR

This paper introduces an efficient iterative method to compute a generalized median graph from a set of graphs, addressing the NP-hard challenge with a block coordinate descent approach that optimizes node and edge labelings.

## Contribution

It proposes a novel block coordinate descent algorithm for median graph computation that handles labeling on both nodes and edges, improving efficiency.

## Key findings

- Demonstrates efficiency through experiments on multiple datasets
- Handles labeling on nodes and edges effectively
- Provides a clear optimization framework for median graph computation

## Abstract

Computing a graph prototype may constitute a core element for clustering or classification tasks. However, its computation is an NP-Hard problem, even for simple classes of graphs. In this paper, we propose an efficient approach based on block coordinate descent to compute a generalized median graph from a set of graphs. This approach relies on a clear definition of the optimization process and handles labeling on both edges and nodes. This iterative process optimizes the edit operations to perform on a graph alternatively on nodes and edges. Several experiments on different datasets show the efficiency of our approach.