Nontrivial lower bounds for some NP-problems on directed graphs
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.
KeywordsSingular Point Directed Graph Linear Time Acyclic Directed Graph Turing Machine
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