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 -