  In the worst-case distributed source coding (DSC) problem of [1], the smaller
cardinality of the support-set describing the correlation in informant data,
may neither imply that fewer informant bits are required nor that fewer
informants need to be queried, to finish the data-gathering at the sink. It is
important to formally address these observations for two reasons: first, to
develop good worst-case information measures and second, to perform meaningful
worst-case information-theoretic analysis of various distributed data-gathering
problems. Towards this goal, we introduce the notions of bit-compressibility
and informant-compressibility of support-sets. We consider DSC and distributed
function computation problems and provide results on computing the bit- and
informant- compressibilities regions of the support-sets as a function of their
cardinality.
