Fast-Mixed Searching on Graphs
نویسنده
چکیده
We introduce the fast-mixed search model, which is a combination of the fast search model and the mixed search model. We establish relations between the fast-mixed search problem and other graph search problems. We also establish relations between the fast-mixed search problem and the inducedpath cover problem. We present linear-time algorithms for computing the fast-mixed search number and optimal search strategies of some classes of graphs, including trees, cacti, and interval graphs. We prove that the fast-mixed search problem is NP-complete, and it remains NP-complete for outerplanar graphs with maximum degree 3. We also proved that, given a graph G with k leaves, the problem of determining whether the fast-mixed search number of G is dk/2e is NP-complete, and it remains NP-complete for graphs with maximum degree 4.
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