Complexity of Linear Connectivity Problems in Directed Hypergraphs

  • Mayur Thakur
  • Rahul Tripathi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3328)


We introduce a notion of linear hyperconnection (formally denoted L-hyperpath) between nodes in a directed hypergraph and relate this notion to existing notions of hyperpaths in directed hypergraphs. We observe that many interesting questions in problem domains such as secret transfer protocols, routing in packet filtered networks, and propositional satisfiability are basically questions about existence of L-hyperpaths or about cyclomatic number of directed hypergraphs w.r.t. L-hypercycles (the minimum number of hyperedges that need to be deleted to make a directed hypergraph free of L-hypercycles). We prove that the L-hyperpath existence problem, the cyclomatic number problem, the minimum cyclomatic set problem, and the minimal cyclomatic set problem are each complete for a different level (respectively, NP, \({\it \Sigma}^{p}_{2}\), \({\it \Pi}^{p}_{2}\), and DP) of the polynomial hierarchy.


Directed Graph Problem Domain Simple Path Simple Cycle Reachability Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Mayur Thakur
    • 1
  • Rahul Tripathi
    • 2
  1. 1.Dept. of Computer ScienceUniversity of Missouri–RollaRollaUSA
  2. 2.Dept. of Computer ScienceUniversity of RochesterRochesterUSA

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