# An Algorithm for Subgraph Isomorphism

@article{Ullmann1976AnAF, title={An Algorithm for Subgraph Isomorphism}, author={Julian R. Ullmann}, journal={Journal of the ACM (JACM)}, year={1976}, volume={23}, pages={31 - 42} }

Subgraph isomorphism can be determined by means of a brute-force tree-search enumeration procedure. In this paper a new algorithm is introduced that attains efficiency by inferentially eliminating successor nodes in the tree search. To assess the time actually taken by the new algorithm, subgraph isomorphism, clique detection, graph isomorphism, and directed graph isomorphism experiments have been carried out with random and with various nonrandom graphs. A parallel asynchronous logic-in-memory…

## 2,212 Citations

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This paper attempts to parallelize a fast serial subgraph isomorphism library, VFLib, which uses backtracking search to find a solution, and uses conditional copying to achieve near-linear speedup with the number of CPU cores on random graphs and reasonable performance on parasitic inputs.

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This paper's ongoing work on designing a parallel algorithm for the subgraph (and graph) isomorphism problem is presented, which addresses challenges commonly faced when attempting to obtain a parallel algorithms for isomorphisms.

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Search Strategies for Subgraph Isomorphism Algorithms

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- 2014

The impact of various search strategies on the efficiency of two algorithms are investigated, the first being the Ullmann's algorithm and the second one the recently proposed improvement of Ullman's algorithm.

A consistency rule for graph isomorphism problem

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- 2012

The proposed consistency rule is able to prune as early as possible unfruitful branches of the tree-search which leads to reduce the practical time complexity.

OPTIMIZED BACKTRACKING FOR SUBGRAPH ISOMORPHISM

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Two new algorithms for subgraph isomorphism problem for labeled graphs based on modified adjacency list that are competitive with classic Ullman’s algorithm and more recent VF2 are presented.

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