Maximum Tree-Packing in Time O(n5/2)

The problem of determining the maximum number of node-disjoint subtrees of a tree T on nt nodes isomorphic to a tree S on ns nodes is shown to be solvable in time O(n s 3/2 nt). The same asymptotic bounds are observed for the corresponding problems where topological imbedding and subgraph homeomorphism are respectively substituted for subgraph isomorphism.

[1]  Rakesh M. Verma,et al.  An Analysis of a Good Algorithm for the Subtree Problem, Corrected , 1989, SIAM J. Comput..

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  Frank Harary,et al.  Graph Theory , 2016 .

[4]  David G. Kirkpatrick,et al.  On the Complexity of General Graph Factor Problems , 1981, SIAM J. Comput..

[5]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[6]  Pavol Hell,et al.  Packings by complete bipartite graphs , 1986 .

[7]  Marek Karpinski,et al.  Subtree Isomorphism is NC Reducible to Bipartite Perfect Matching , 1989, Inf. Process. Lett..

[8]  David G. Kirkpatrick,et al.  On Generalized Matching Problems , 1981, Inf. Process. Lett..

[9]  David G. Kirkpatrick,et al.  On the completeness of a generalized matching problem , 1978, STOC.

[10]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[11]  David G. Kirkpatrick,et al.  Packings by cliques and by finite families of graphs , 1984, Discret. Math..

[12]  Robin Thomas,et al.  On the complexity of finding iso- and other morphisms for partial k-trees , 1992, Discret. Math..

[13]  Francine Berman,et al.  Generalized Planar Matching , 1990, J. Algorithms.

[14]  D. Matula.  Subtree Isomorphism in O(n5/2) , 1978 .

[15]  Steven W. Reyner,et al.  An Analysis of a Good Algorithm for the Subtree Problem , 1977, SIAM J. Comput..

[16]  Naomi Nishimura,et al.  Sequential and Parallel Algorithms for Embedding Problems on Classes of Partial k-Trees , 1994, SWAT.