# Largest Common Subtree (Graph Isomorphism Problem)

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## Description

Find a largest tree which occurs as a common subgraph in a given collection of trees.

## Related Problems

Generalizations: Graph Isomorphism, General Graphs

Subproblem: Subtree Isomorphism

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

## Parameters

$n$: number of vertices in the largest tree in the collection

## 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 constants $d \geq {2}$, target on two rooted trees of size at most $n$, degree $d$, and height $h \leq \log_d n + O(\log \log n)$ cannot be solved in truly subquadtratic $O(n^{2-\epsilon})$ time |
2018 | https://dl.acm.org/doi/pdf/10.1145/3093239 | link |