An exact algorithm for subgraph homeomorphism

Andrzej Lingas, Martin Wahlen
2009 Journal of Discrete Algorithms  
The subgraph homeomorphism problem is to decide if there is an injective mapping of the vertices of a pattern graph into vertices of a host graph so that the edges of the pattern graph can be mapped into (internally) vertex-disjoint paths in the host graph. The restriction of subgraph homeomorphism where an injective mapping of the vertices of the pattern graph into vertices of the host graph is already given in the input instance is termed fixed-vertex subgraph homeomorphism. We show that
more » ... -vertex subgraph homeomorphism for a pattern graph on p vertices and a host graph on n vertices can be solved in time 2 n−p n O (1) or in time 3 n−p n O (1) and polynomial space. In effect, we obtain new non-trivial upper bounds on the time complexity of the problem of finding k vertex-disjoint paths and general subgraph homeomorphism. .se (A. Lingas), martin@cs.lth.se (M. Wahlen). 1 This upper bound can be marginally improved by using the rectangular matrix multiplication instead of the square one. 1570-8667/$ -see front matter
doi:10.1016/j.jda.2008.10.003 fatcat:nh7hy24fdrcrlbv242dpjtlabm