@article{krishnan_mathew_kalyanasundaram_2022, 
  title={Pliable Index Coding via Conflict-Free Colorings of Hypergraphs}, 
  abstractNote={In the pliable index coding (PICOD) problem, a server is to serve multiple
clients, each of which possesses a unique subset of the complete message set as
side information and requests a new message which it does not have. The goal of
the server is to do this using as few transmissions as possible. This work
presents a hypergraph coloring approach to the scalar PICOD problem. A
conflict-free coloring of a hypergraph is known from literature as an
assignment of colors to its vertices so that each hyperedge of the graph
contains one uniquely colored vertex. For a given PICOD problem represented by
a hypergraph consisting of messages as vertices and request-sets as hyperedges,
we present achievable PICOD schemes using conflict-free colorings of the PICOD
hypergraph. Various graph theoretic parameters arising out of such colorings
(and some new coloring variants) then give a number of upper bounds on the
optimal PICOD length, which we study in this work. Suppose the PICOD hypergraph
has m vertices and n hyperedges, where every hyperedge overlaps with at
most Γ other hyperedges. We show easy to implement randomized algorithms
for the following: (a) For the single request case, we give a PICOD of length
O(log^2Γ). This result improves over known achievability results for
some parameter ranges, (b) For the t-request case, we give an MDS code of
length max(O(logΓlog m), O(t log m)). Further if the hyperedges
(request sets) are sufficiently large, we give a PICOD of the same length as
above, which is not based on MDS construction. In general, this gives an
improvement over prior achievability results. Our codes are of near-optimal
length (up to a multiplicative factor of log t).}, 
  author={Krishnan and Mathew and Kalyanasundaram}, 
  year={2022}, 
  month={Dec}
  }