graph_approach.py

def graph_approach(df, key='person_id', start='start', end='end'):
    start = df[start]values
    end = df[end]values
    person_id = df[person_id]values
    graph = (start <= end[:, None]) & (end >= start[:, None]) & (person_id == person_id[:, None])
    n_components, indices = connected_components(graph, directed=False)
    return df.groupby(indices).aggregate({'person_id': 'first', 'start': 'min','end': 'max'})