Under Linux, how do I find out which process is using the swap space more?
You can use Procpath (author here), to simplify parsing of VmSwap from /proc/$PID/status.
$ procpath record -f stat,cmdline,status -r 1 -d db.sqlite
$ sqlite3 -column db.sqlite \
'SELECT status_name, status_vmswap FROM record ORDER BY status_vmswap DESC LIMIT 5'
Web Content 192136
okular 186872
thunderbird 183692
Web Content 143404
MainThread 86300
You can also plot VmSwap of processes of interest over time like this. Here I'm recording my Firefox process tree while opening a couple tens of tabs along with statrting a memory-hungry application to try to cause it to swap (which wasn't convincing for Firefox, but your kilometrage may vary).
$ procpath record -f stat,cmdline,status -i 1 -d db2.sqlite \
'$..children[?(@.stat.pid == 6029)]'
# interrupt by Ctrl+C
$ procpath plot -d db2.sqlite -q cpu --custom-value-expr status_vmswap \
--title "CPU usage, % vs Swap, kB"