Abstract
Is it possible to force a graph search algorithm to visit a selected vertex as last? Corneil, Köhler, and Lanlignel showed that this end-vertex decision problem is NP-complete for Lexicographic Breadth-First Search (LexBFS). Charbit, Habib, and Mamcarz extended the intractability result, and showed that the end-vertex problem is hard also for BFS, DFS, and LexDFS. We ask for positive results, and study algorithmic and combinatorial questions. We show that the end-vertex problem for BFS and DFS can be solved in \(\mathcal{O}^*(2^n)\) time, hereby improving upon the straightforward and currently best known running-time bound of \(\mathcal{O}^*(n!)\). We also determine conditions that preserve end-vertices in subgraphs when extending to larger graphs. Such results are of interest in algorithm design, when applying techniques such as dynamic programming and divide-and-conquer.
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Kratsch, D., Liedloff, M., Meister, D. (2015). End-Vertices of Graph Search Algorithms. In: Paschos, V., Widmayer, P. (eds) Algorithms and Complexity. CIAC 2015. Lecture Notes in Computer Science(), vol 9079. Springer, Cham. https://doi.org/10.1007/978-3-319-18173-8_22
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DOI: https://doi.org/10.1007/978-3-319-18173-8_22
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