论文信息 - Faster Algorithms for Subgraph Isomorphism of \sl k -Connected Partial \sl k -Trees

Faster Algorithms for Subgraph Isomorphism of \sl k -Connected Partial \sl k -Trees

Abstract. The problem of determining whether a k -connected partial k -tree is isomorphic to a subgraph of another partial k -tree is shown to be solvable in time O(nk+2) . The presented time-bounds considerably improve the corresponding bounds known in the literature. They rely in part on a new characterization of width-k tree-decomposition of k -connected partial k -trees.

Andrzej Lingas | Anders Dessmark | Andrzej Proskurowski

[1] M. Karpinski,et al. Subtree Isomorphism and Bipartite Perfect Matching are Mutually $NC$-Reducible , 1986 .

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

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

[4] Naomi Nishimura,et al. Characterizing the Complexity of Subgraph Isomorphism for Graphs of Bounded Path-Width , 1996, STACS.

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

[6] Andrzej Lingas. Subgraph Isomorphism for Biconnected Outerplanar Graphs in Cubic Time , 1989, Theor. Comput. Sci..

[7] Andrzej Lingas,et al. Faster Algorithms for Subgraph Isomorphism of k-Connected Partial k-Trees , 1996, ESA.

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

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

[10] Hans L. Bodlaender,et al. Dynamic Programming on Graphs with Bounded Treewidth , 1988, ICALP.

[11] Hans L. Bodlaender,et al. A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC.

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

[13] Maciej M. Syslo,et al. Plane Embeddings of 2-trees and Biconnected Partial 2-Trees , 1996, SIAM J. Discret. Math..