Belangrijkste concepten
The last-in-tree recognition problem for Generic Search is NP-complete, and this result is used to show that the Intermezzo Problem remains NP-complete even when the partial order forms a tree of bounded height.
Samenvatting
The paper investigates the complexity of the last-in-tree recognition problem for Generic Search (GS) and its connection to the Intermezzo Problem.
Key insights:
The last-in-tree recognition problem for GS is NP-complete, even when restricted to rooted spanning trees of height 5. This is surprising as other graph search problems for GS are solvable in polynomial time.
The NP-completeness of the last-in-tree recognition problem for GS is used to show that the Intermezzo Problem remains NP-complete even when the partial order forms a cs-tree (a tree-like partial order) of bounded height.
In contrast, an XP algorithm is provided for the Intermezzo Problem when parameterized by the width of the partial order, and it is shown that this algorithm is asymptotically optimal under the Exponential Time Hypothesis.
The paper first introduces the necessary concepts and definitions, including graph searches, partial orders, and the last-in-tree recognition problem. It then proves the NP-completeness of the last-in-tree recognition problem for GS and uses this result to establish the NP-completeness of the Intermezzo Problem for cs-trees of bounded height. Finally, it presents the XP algorithm for the Intermezzo Problem parameterized by the width of the partial order.