Unicast-Uniprior Index Coding Problems: Minrank and Criticality

Abstract: An index coding problem is called unicast-uniprior when each receiver demands a unique subset of messages while knowing another unique subset of messages apriori as side-information. In this work, we give an algorithm to compute the minrank of a unicast-uniprior problem. The proposed algorithm greatly simplifies the computation of minrank for unicast-uniprior problem settings, over the existing method whose complexity is exponential in the number of messages. First, we establish some properties that are exclusive to the fitting matrix of a unicast-uniprior problem. Further, these properties are used to lay down the algorithm that computes the minrank.