In on-line computation, the instance of the problem dealt is notentirely known from the beginning of the solution process, but itis revealed step-by-step. In this paper we deal with on-lineindependent set. On-line models studied until now for this problemsuppose that the input graph is initially empty and revealedeither vertex-by-vertex, or cluster-by-cluster. Here we present anew on-line model quite different to the ones already studied. Itassumes that a superset of the final graph is initially present(in our case the complete graph on the order n of the finalgraph) and edges are progressively removed until the achievementof the final graph. Next, we revisit the model introduced in[Demange, Paradon and Paschos, Lect. Notes Comput. Sci.1963 (2000)326–334] and study relaxations assuming that somepaying backtracking is allowed.
