A polynomial-time algorithm for pliable index coding

Linqi Song, Christina Fragouli

Abstract: Pliable index coding considers a server with m messages and n clients where each client has as side information a subset of the messages. We seek to minimize the number of transmissions the server should make, so that each client receives (any) one message she does not already have. Previous work has shown that the server can achieve this using at most O(log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (n)) transmissions and needs at least Ω(log(n)) transmissions in the worst case, but finding a code of optimal length is NP-hard. In this paper, we design a polynomial-time algorithm that uses less than O(log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (n)) transmissions, i.e., almost worst-case optimal. We also establish a connection between the pliable index coding problem and the minrank problem over a family of mixed matrices.