PostgreSQL: how do I group rows by 'nearby' timestamps - postgresql

Question

Considering the following simplified situation:
create table trans
(
id integer not null
, tm timestamp without time zone not null
, val integer not null
, cus_id integer not null
);
insert into trans
(id, tm, val, cus_id)
values
(1, '2017-12-12 16:42:00', 2, 500) --
,(2, '2017-12-12 16:42:02', 4, 501) -- <--+---------+
,(3, '2017-12-12 16:42:05', 7, 502) -- |dt=54s |
,(4, '2017-12-12 16:42:56', 3, 501) -- <--+ |dt=59s
,(5, '2017-12-12 16:43:00', 2, 503) -- |
,(6, '2017-12-12 16:43:01', 5, 501) -- <------------+
,(7, '2017-12-12 16:43:15', 6, 502) --
,(8, '2017-12-12 16:44:50', 4, 501) --
;
I want to group rows by cus_id, but also where the interval between time stamps of consecutive rows for the same cus_id is less than 1 minute.
In the example above this applies to rows with id's 2, 4 and 6. These rows have the same cus_id (501) and have intervals below 1 minute. The interval id{2,4} is 54s and for id{2,6} it is 59s. The interval id{4,6} is also below 1 minute, but it is overridden by the larger interval id{2,6}.
I need a query that gives me the output:
cus_id | tm | val
--------+---------------------+-----
501 | 2017-12-12 16:42:02 | 12
(1 row)
The tm value would be the tm of the first row, i.e. with the lowest tm. The val would be the sum(val) of the grouped rows.
In the example 3 rows are grouped, but that could also be 2, 4, 5, ...
For simplicity, I only let the rows for cus_id 501 have nearby time stamps, but in my real table, there would be a lot more of them. It contains 20M+ rows.
Is this possible?

Answer 1

Naive (subobtimal) solution using a CTE
(a faster approach would avoid the CTE, replacing it by a joined subquery or maybe even use a window function) :
-- Step one: find the start of a cluster
-- (the start is everything after a 60 second silence)
WITH starters AS (
SELECT * FROM trans tr
WHERE NOT EXISTS (
SELECT * FROM trans nx
WHERE nx.cus_id = tr.cus_id
AND nx.tm < tr.tm
AND nx.tm >= tr.tm -'60sec'::interval
)
)
-- SELECT * FROM starters ; \q
-- Step two: join everything within 60sec to the starter
-- and aggregate the clusters
SELECT st.cus_id
, st.id AS id
, MAX(tr.id) AS max_id
, MIN(tr.tm) AS first_tm
, MAX(tr.tm) AS last_tm
, SUM(tr.val) AS val
FROM trans tr
JOIN starters st ON st.cus_id = tr.cus_id
AND st.tm <= tr.tm AND st.tm > tr.tm -'60sec'::interval
GROUP BY 1,2
ORDER BY 1,2
;