The computational complexity of the minimum weight processor assignment problem

  • Authors:

  • Hajo J. Broersma;Daniel Paulusma;Gerard J. M. Smit;Frank Vlaardingerbroek;Gerhard J. Woeginger

  • Affiliations:

  • Department of Computer Science, University of Durham, Science Labs, Durham, England;Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands;Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands;Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands;Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

  • Venue:
  • WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
  • Year:
  • 2004

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Abstract

In portable multimedia systems a number of communicating tasks has to be performed on a set of heterogeneous processors in an energy-efficient way. We model this problem as a graph optimization problem, which we call the minimum weight processor assignment problem. We show that our setting generalizes several problems known in literature, including minimum multiway cut, graph k-colorability, and minimum (generalized) vertex covering. We show that the minimum weight processor assignment problem is NP-hard, even when restricted to instances where the (process) graph is a bipartite graph with maximum degree at most 3, or with only two processors, or with arbitrarily small weight differences, or with only two different edge weights. For graphs with maximum degree at most 2 (or in fact the larger class of degree-2-contractible graphs) we give a polynomial time algorithm. Finally we generalize this algorithm into an exact (but not efficient) algorithm for general graphs.