Nontrivial lower bounds for some NP-problems on directed graphs

  • Solomampionona Ranaivoson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 533)


NP-complete problems are believed to be not in P. But only a very few NP-complete problems, and none concerning graph theory, are proved to have a nontrivial time lower bound (i.e. not to be solvable in linear time on a DTM (i.e. deterministic Turing machine). A problem L ε NP is linearly NP-complete if any problem in Ntime (n) can be reduced to it in linear time on a DTM. It follows from the separation result between deterministic and nondeterministic linear-time complexity classes [PPST83], that a linearly NP-complete problem has a nontrivial time lower bound. We present in this paper the first natural problems on graphs which are linearly NP-complete.


Singular Point Directed Graph Linear Time Acyclic Directed Graph Turing Machine 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Solomampionona Ranaivoson
    • 1
  1. 1.Laboratoire d'Informatique de l'Université de CaenCaen cedexFrance

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