Clearing Connections by Few Agents

  • Christos Levcopoulos
  • Andrzej Lingas
  • Bengt J. Nilsson
  • Paweł Żyliński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8496)


We study the problem of clearing connections by agents placed at some vertices in a directed graph. The agents can move only along directed paths. The objective is to minimize the number of agents guaranteeing that any pair of vertices can be connected by a underlying undirected path that can be cleared by the agents. We provide several results on the hardness, approximability and parameterized complexity of the problem. In particular, we show it to be: NP-hard, 2-approximable in polynomial-time, and solvable exactly in O(αn 322 α ) time, where α is the number of agents in the solution. In addition, we give a simple linear-time algorithm optimally solving the problem in digraphs whose underlying graphs are trees. Finally, we discuss a related problem, where the task is to clear with a minimum number of agents a subgraph of the underlying graph containing its spanning tree. We show that this problem also admits a 2-approximation in polynomial time.


clearing paths NP-hardness approximation parametrized complexity 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Christos Levcopoulos
    • 1
  • Andrzej Lingas
    • 1
  • Bengt J. Nilsson
    • 2
  • Paweł Żyliński
    • 3
  1. 1.Lund UniversityLundSweden
  2. 2.Malmö UniversityMalmöSweden
  3. 3.University of GdańskGdańskPoland

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