Spatial structures and their dynamics turned out to be ideal candidates for data storage and information processing. Algorithmic design can unequivocally benefit from exploitation of the features provided by computing in space. The corresponding field, to which we refer to as morphological algorithmics, constitutes a promising branch within membrane computing when considering spatial structures found in biological compartments and conformations of macromolecules. Plasticity of receptors residing on cell membranes as well as agility of transfer RNA containers exhibits two forms of morphology worth to be utilised for computing purposes. To this end, we introduce two novel approaches to solve by morphological algorithms the exact set cover problem known to be NP-complete. Both approaches overcome the insufficiencies caused by the need of a pre-compiled exponential workspace. Moreover, they combine the capability of self-organization with an exhaustive search. We present both algorithms along with consistent simulation case studies carried out using P-Lingua and SRSim.