How to join two dataframes for which column values are within a certain range?

First use IntervalIndex to create a reference index based on the interval of interest, then use get_indexer to slice the dataframe which contains the discrete events of interest.

idx = pd.IntervalIndex.from_arrays(df_2['start'], df_2['end'], closed='both')
event = df_2.iloc[idx.get_indexer(df_1.timestamp), 'event']

event
0    E1
1    E2
1    E2
1    E2
2    E3
Name: event, dtype: object

df_1['event'] = event.to_numpy()
df_1
            timestamp         A         B event
0 2016-05-14 10:54:33  0.020228  0.026572    E1
1 2016-05-14 10:54:34  0.057780  0.175499    E2
2 2016-05-14 10:54:35  0.098808  0.620986    E2
3 2016-05-14 10:54:36  0.158789  1.014819    E2
4 2016-05-14 10:54:39  0.038129  2.384590    E3

Reference: A question on IntervalIndex.get_indexer.

Option 1

idx = pd.IntervalIndex.from_arrays(df_2['start'], df_2['end'], closed='both')
df_2.index=idx
df_1['event']=df_2.loc[df_1.timestamp,'event'].values

Option 2

df_2['timestamp']=df_2['end']
pd.merge_asof(df_1,df_2[['timestamp','event']],on='timestamp',direction ='forward',allow_exact_matches =True)
Out[405]: 
            timestamp         A         B event
0 2016-05-14 10:54:33  0.020228  0.026572    E1
1 2016-05-14 10:54:34  0.057780  0.175499    E2
2 2016-05-14 10:54:35  0.098808  0.620986    E2
3 2016-05-14 10:54:36  0.158789  1.014819    E2
4 2016-05-14 10:54:39  0.038129  2.384590    E3

You can use the module pandasql

import pandasql as ps

sqlcode = '''
select df_1.timestamp
,df_1.A
,df_1.B
,df_2.event
from df_1 
inner join df_2 
on d1.timestamp between df_2.start and df2.end
'''

newdf = ps.sqldf(sqlcode,locals())

One simple solution is create interval index from start and end setting closed = both then use get_loc to get the event i.e (Hope all the date times are in timestamps dtype )

df_2.index = pd.IntervalIndex.from_arrays(df_2['start'],df_2['end'],closed='both')
df_1['event'] = df_1['timestamp'].apply(lambda x : df_2.iloc[df_2.index.get_loc(x)]['event'])

Output :

            timestamp         A         B event
0 2016-05-14 10:54:33  0.020228  0.026572    E1
1 2016-05-14 10:54:34  0.057780  0.175499    E2
2 2016-05-14 10:54:35  0.098808  0.620986    E2
3 2016-05-14 10:54:36  0.158789  1.014819    E2
4 2016-05-14 10:54:39  0.038129  2.384590    E3