On the Simultaneous Minimum Spanning Trees Problem
| Autor: | Martin Töpfer, Jana Novotná, Jakub Tětek, Matěj Konečný, Jakub Pekárek, Stanislav Kučera, Martin Smolík |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Algorithms and Discrete Applied Mathematics ISBN: 9783319741796 CALDAM |
| DOI: | 10.1007/978-3-319-74180-2_20 |
| Popis: | Simultaneous Embedding with Fixed Edges (SEFE) [1] is a problem where given k planar graphs we ask whether they can be simultaneously embedded so that the embedding of each graph is planar and common edges are drawn the same. Problems of SEFE type have inspired questions of Simultaneous Geometrical Representations and further derivations. Based on this motivation we investigate the generalization of the simultaneous paradigm on the classical combinatorial problem of minimum spanning trees. Given k graphs with weighted edges, such that they have a common intersection, are there minimum spanning trees of the respective graphs such that they agree on the intersection? We show that the unweighted case is polynomial-time solvable while the weighted case is only polynomial-time solvable for \(k=2\) and it is \(\mathsf {NP}\)-complete for \(k\ge 3\). |
| Databáze: | OpenAIRE |
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