A hypocoloring model for batch scheduling

  • Authors:

  • D. de Werra;M. Demange;J. Monnot;V. Th. Paschos

  • Affiliations:

  • Ecole Polytechnique Fédérale de Lausanne, EPFL, Switzerland;ESSEC, Department of SID, France;LAMSADE CNRS, Université Paris-Dauphine, Place de Marechal de Lattre de Tassigny, Paris, Ceder 75775, France;LAMSADE CNRS, Université Paris-Dauphine, Place de Marechal de Lattre de Tassigny, Paris, Ceder 75775, France

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2005

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Abstract

Starting from a batch scheduling problem, we consider a weighted subcoloring in a graph G; each node v, has a weight w(v); each color class S is a subset of nodes which generates a collection of node disjoint cliques. The weight w(S) is defined as max{w(K) = Σv ∈ K w(v)|K ∈ S}. In the scheduling problem, the completion time is given by Σi = 1k w(Si) where J = (S1,...., Sk) is a partition of the node set of graph G into color classes as defined above. Properties of such colorings concerning special classes of graphs (line graphs of cacti, block graphs) are stated; complexity and approximability results are presented. The associated decision problem is shown to be NP-complete for bipartite graphs with maximum degree at most 39 and triangle-free planar graphs with maximum degree k for any k ≥ 3. Polynomial algorithms are given for graphs with maximum degree two and for the forests with maximum degree k. An (exponential) algorithm based on a simple separation principle is sketched for graphs without triangles.