On-line models and algorithms for max independent set

LAMSADE, Université Paris-Dauphine, 75775 Paris Cedex 16, France; e-mail: {escoffier,paschos}@lamsade.dauphine.fr

Received: 11 November 2003

Abstract

In on-line computation, the instance of the problem dealt is not entirely known from the beginning of the solution process, but it is revealed step-by-step. In this paper we deal with on-line independent set. On-line models studied until now for this problem suppose that the input graph is initially empty and revealed either vertex-by-vertex, or cluster-by-cluster. Here we present a new on-line model quite different to the ones already studied. It assumes that a superset of the final graph is initially present (in our case the complete graph on the order n of the final graph) and edges are progressively removed until the achievement of 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 some paying backtracking is allowed.