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Many problems in graph algorithms may be solved efficiently on graphs of low pathwidth, by using dynamic programming on
???
exponential time.
by the pathwidth.
NP-hard optimization problems.
the complexity of the input.
a path-decomposition of the graph.
On graphs of bounded pathwidth, this approach leads to fixed-parameter tractable algorithms, parametrized
???
exponential time.
by the pathwidth.
NP-hard optimization problems.
the complexity of the input.
a path-decomposition of the graph.
The same dynamic programming method also can be applied to graphs with unbounded pathwidth, leading to algorithms that solve unparametrized graph problems in
???
exponential time.
by the pathwidth.
NP-hard optimization problems.
the complexity of the input.
a path-decomposition of the graph.
A similar approach leads to improved exponential-time algorithms for the maximum cut and minimum dominating set problems in cubic graphs,and for several other
???
exponential time.
by the pathwidth.
NP-hard optimization problems.
the complexity of the input.
a path-decomposition of the graph.
An algorithm is said to be solvable in polynomial time if the number of steps required to complete the algorithm for a given input is for some nonnegative integer, where is
???
exponential time.
by the pathwidth.
NP-hard optimization problems.
the complexity of the input.
a path-decomposition of the graph.
Check
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