There are a couple of ways to help jet fighters take off with
short runways. One of the most common method is the rocket assisted
takeoff where rockets are stripped onto the fusalage of the
aircraft and ignite during take off. This was common with the F104
StarFighter. Other common methods including using of ramps (like
the ramps used for some aircraft carriers today. With some sort of
portable, quick install catapult systems, an jet can take off less
than 400m. Aircrafts of the size of the F5s and Vipers should be
able to take off shorter than 400m if they can be launch from some
sort of land based catapult system.
While in terms of having the jets to take off if the runways in
Paya Lebar, Tengah and Changi are taken out, the roads systems are
the quickest means. There are also a couple of alternatives
including, using large fields (usually more suited for Russian made
jets because they come with mud flaps and the intake have special
shields as in the case of Mig29, to prevent FOD objects from being
sucked into the engines).
Singapore could also have underground runways or tunnels where part
of the runways are sunk underground and only about 200m above
ground, thus allowing the fighters roll some 400m or more protected
and the last 200m for final take off. Once again, these tunnels
have to be relatively straight and wide enuff, plus they also must
have real good exhaust fans too... 
Lastly, RSAF would have also invested in acquiring runway repair
vehicles where they could quickly cover bombed out holes, level and
compact the filled-in holes and temporary tarmac it within a very
short period of time.
