Exploiting bounded signal flow for graph orientation based on cause-effect pairs

  • Authors:

  • Britta Dorn;Falk Hüffner;Dominikus Krüger;Rolf Niedermeier;Johannes Uhlmann

  • Affiliations:

  • Fakultät für Mathematik und Wirtschaftswissenschaften, Universität Ulm, Ulm, Germany;Institut für Informatik, Humboldt-Universität zu Berlin, Berlin, Germany;Institut f¨r Theoretische Informatik, Universität Ulm, Ulm, Germany;Institut für Softwaretechnik und Theoretische Informatik, Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, Berlin, Germany

  • Venue:
  • TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
  • Year:
  • 2011

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Abstract

We consider the following problem: Given an undirected network and a set of sender-receiver pairs, direct all edges such that the maximum number of "signal flows" defined by the pairs can be routed respecting edge directions. This problem has applications in communication networks and in understanding protein interaction based cell regulation mechanisms. Since this problem is NP-hard, research so far concentrated on polynomial-time approximation algorithms and tractable special cases. We take the viewpoint of parameterized algorithmics and examine several parameters related to the maximum signal flow over vertices or edges. We provide several fixed-parameter tractability results, and in one case a sharp complexity dichotomy between a linear-time solvable case and a slightly more general NP-hard case. We examine the value of these parameters for several real-world network instances. For many relevant cases, the NP-hard problem can be solved to optimality. In this way, parameterized analysis yields both deeper insight into the computational complexity and practical solving strategies.