Are Guessing, Source Coding and Tasks Partitioning Birds of A Feather?

This paper establishes a close relationship among the four information theoretic problems, namely Campbell source coding, Arikan guessing, Huleihel et al. memoryless guessing and Bunte and Lapidoth tasks' partitioning problems in the IID-lossless case. We first show that the aforementioned problems are mathematically related via a general moment minimization problem whose optimum solution is given in terms of Renyi entropy.