Subtree Isomorphism (Graph Isomorphism Problem)

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Determine whether a given tree is contained within another tree.

Related Problems

Generalizations: Largest Common Subtree

Related: Graph Isomorphism, General Graphs, Graph Isomorphism, Bounded Number of Vertices of Each Color, Graph Isomorphism, Trivalent Graphs, Graph Isomorphism, Bounded Vertex Valences


$n$: number of vertices in the larger graph

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
McKay 1981 $O((m1 + m2)n^{3} + m2 n^{2} L)$ ${2}mn+{10}n+m+(m+{4})K+{2}mL$ Exact Deterministic Time
Schmidt & Druffel 1976 $O(n*n!)$ $O(n^{2})$ Exact Deterministic Time
Babai 2017 {2}^{$O(\log n)$^3} Exact Deterministic Time

Reductions FROM Problem

Problem Implication Year Citation Reduction
OV assume: OVH
then: for all $d \geq {2}$, target on two rooted unordered trees of size $O(n)$, degree $d$, and height $h \leq {2}\log_d n + O(\log \log n)$ cannot be solved in truly subquadratic $O(n^{2-\epsilon})$ time
2018 link