# Unicast-Uniprior Index Coding Problems: Minrank and Criticality

## TL;DR

This paper introduces an efficient algorithm for computing the minrank of unicast-uniprior index coding problems, significantly simplifying the process compared to previous exponential-time methods.

## Contribution

The authors present a novel polynomial-time algorithm leveraging unique properties of unicast-uniprior problems' fitting matrices to compute minrank.

## Key findings

- Algorithm reduces computation complexity from exponential to polynomial.
- Properties of fitting matrices are key to the new algorithm.
- Simplifies analysis and design of index coding schemes for unicast-uniprior problems.

## 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.