1 research outputs found
Computing -Labeling with Combined Parameters
Given a graph, an -labeling of the graph is an assignment from
the vertex set to the set of nonnegative integers such that for any pair of
vertices if and are adjacent, and if and are at distance . The -labeling problem is
to minimize the span of (i.e.,). It is known to be NP-hard even for graphs of maximum degree
or graphs with tree-width 2, whereas it is fixed-parameter tractable with
respect to vertex cover number. Since vertex cover number is a kind of the
strongest parameter, there is a large gap between tractability and
intractability from the viewpoint of parameterization. To fill up the gap, in
this paper, we propose new fixed-parameter algorithms for -Labeling by
the twin cover number plus the maximum clique size and by the tree-width plus
the maximum degree. These algorithms reduce the gap in terms of several
combinations of parameters