TY - GEN
T1 - Finding smallest supertrees under minor containment
AU - Nishimura, Naomi
AU - Ragde, Prabhakar
AU - Thilikos, Dimitrios M.
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.
PY - 1999
Y1 - 1999
N2 - The diversity of application areas relying on tree-structured data results in a wide interest in algorithms which determine differences or similarities among trees. One way of measuring the similarity between trees is to find the smallest common superstructure or supertree, where common elements are typically defined in terms of a mapping or embedding. In the simplest case, a supertree will contain exact copies of each input tree, so that for each input tree, each vertex of a tree can be mapped to a vertex in the supertree such that each edge maps to the corresponding edge. More general mappings allow for the extraction of more subtle common elements captured by looser definitions of similarity. We consider supertrees under the general mapping of minor containment. Minor containment generalizes both subgraph isomorphism and topological embedding; as a consequence of this generality, however, it is NP-complete to determine whether or not G is a minor of H, even for general trees. By focusing on trees of bounded degree, we obtain an O(n3) algorithm which determines the smallest tree T such that both of the input trees are minors of T, even when the trees are assumed to be unrooted and unordered.
AB - The diversity of application areas relying on tree-structured data results in a wide interest in algorithms which determine differences or similarities among trees. One way of measuring the similarity between trees is to find the smallest common superstructure or supertree, where common elements are typically defined in terms of a mapping or embedding. In the simplest case, a supertree will contain exact copies of each input tree, so that for each input tree, each vertex of a tree can be mapped to a vertex in the supertree such that each edge maps to the corresponding edge. More general mappings allow for the extraction of more subtle common elements captured by looser definitions of similarity. We consider supertrees under the general mapping of minor containment. Minor containment generalizes both subgraph isomorphism and topological embedding; as a consequence of this generality, however, it is NP-complete to determine whether or not G is a minor of H, even for general trees. By focusing on trees of bounded degree, we obtain an O(n3) algorithm which determines the smallest tree T such that both of the input trees are minors of T, even when the trees are assumed to be unrooted and unordered.
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U2 - 10.1007/3-540-46784-x_29
DO - 10.1007/3-540-46784-x_29
M3 - Conference contribution
AN - SCOPUS:84947774171
SN - 3540667318
SN - 9783540667315
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 303
EP - 312
BT - Graph-Theoretic Concepts in Computer Science - 25th International Workshop, WG 1999, Proceedings
A2 - Widmayer, Peter
A2 - Neyer, Gabriele
A2 - Eidenbenz, Stephan
PB - Springer Verlag
T2 - 25th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1999
Y2 - 17 June 1999 through 19 June 1999
ER -