  Recent advancements in graph-based analysis and solutions of instantly
decodable network coding (IDNC) trigger the interest to extend them to more
complicated opportunistic network coding (ONC) scenarios, with limited increase
in complexity. In this paper, we design a simple IDNC-like graph model for a
specific subclass of ONC, by introducing a more generalized definition of its
vertices and the notion of vertex aggregation in order to represent the storage
of non-instantly-decodable packets in ONC. Based on this representation, we
determine the set of pairwise vertex adjacency conditions that can populate
this graph with edges so as to guarantee decodability or aggregation for the
vertices of each clique in this graph. We then develop the algorithmic
procedures that can be applied on the designed graph model to optimize any
performance metric for this ONC subclass. A case study on reducing the
completion time shows that the proposed framework improves on the performance
of IDNC and gets very close to the optimal performance.
