  We use milli-arcsecond accuracy astrometry (proper motions and parallaxes)
from Hipparcos and from radio observations to retrace the orbits of 56 runaway
stars and nine compact objects with distances less than 700 pc, to identify the
parent stellar group. It is possible to deduce the specific formation scenario
with near certainty for two cases. (i) We find that the runaway star zeta
Ophiuchi and the pulsar PSR J1932+1059 originated about 1 Myr ago in a
supernova explosion in a binary in the Upper Scorpius subgroup of the Sco OB2
association. The pulsar received a kick velocity of about 350 km/s in this
event, which dissociated the binary, and gave zeta Oph its large space
velocity. (ii) Blaauw & Morgan and Gies & Bolton already postulated a common
origin for the runaway-pair AE Aur and mu Col, possibly involving the massive
highly-eccentric binary iota Ori, based on their equal and opposite velocities.
We demonstrate that these three objects indeed occupied a very small volume
\sim 2.5Myr ago, and show that they were ejected from the nascent Trapezium
cluster.
  We identify the parent group for two more pulsars: both likely originate in
the 50 Myr old association Per OB3, which contains the open cluster alpha
Persei. At least 21 of the 56 runaway stars in our sample can be linked to the
nearby associations and young open clusters. These include the classical
runaways 53 Arietis (Ori OB1), xi Persei (Per OB2), and lambda Cephei (Cep
OB3), and fifteen new identifications, amongst which a pair of stars running
away in opposite directions from the region containing the lambda Ori cluster.
Other currently nearby runaways and pulsars originated beyond 700 pc, where our
knowledge of the parent groups is very incomplete.
