  Following previous theoretical work by Srinivasan (FOCS 2001) and the first
author (STACS 2006) and a first experimental evaluation on random instances
(ALENEX 2009), we investigate how the recently developed different approaches
to generate randomized roundings satisfying disjoint cardinality constraints
behave when used in two classical algorithmic problems, namely low-congestion
routing in networks and max-coverage problems in hypergraphs.
  We generally find that all randomized rounding algorithms work well, much
better than what is guaranteed by existing theoretical work. The derandomized
versions produce again significantly better rounding errors, with running times
still negligible compared to the one for solving the corresponding LP. It thus
seems worth preferring them over the randomized variants.
  The data created in these experiments lets us propose and investigate the
following new ideas. For the low-congestion routing problems, we suggest to
solve a second LP, which yields the same congestion, but aims at producing a
solution that is easier to round. Experiments show that this reduces the
rounding errors considerably, both in combination with randomized and
derandomized rounding.
  For the max-coverage instances, we generally observe that the greedy
heuristics also performs very good. We develop a strengthened method of
derandomized rounding, and a simple greedy/rounding hybrid approach using
greedy and LP-based rounding elements, and observe that both these improvements
yield again better solutions than both earlier approaches on their own.
  For unit disk max-domination, we also develop a PTAS. Contrary to all other
algorithms investigated, it performs not much better in experiments than in
theory; thus, unless extremely good solutions are to be obtained with huge
computational resources, greedy, LP-based rounding or hybrid approaches are
preferable.
