Isomorphism Test for Digraphs with Weighted Edges

@inproceedings{Piperno2018IsomorphismTF,
  title={Isomorphism Test for Digraphs with Weighted Edges},
  author={Adolfo Piperno},
  booktitle={SEA},
  year={2018}
}
  • A. Piperno
  • Published in SEA 2018
  • Computer Science, Mathematics
Colour refinement is at the heart of all the most efficient graph isomorphism software packages. In this paper we present a method for extending the applicability of refinement algorithms to directed graphs with weighted edges. We use {Traces} as a reference software, but the proposed solution is easily transferrable to any other refinement-based graph isomorphism tool in the literature. We substantiate the claim that the performances of the original algorithm remain substantially unchanged by… 

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References

SHOWING 1-10 OF 19 REFERENCES

Search Space Contraction in Canonical Labeling of Graphs (Preliminary Version)

The individualization-refinement paradigm for computing a canonical labeling and/or the automorphism group of a graph is investigated and a new partition refinement algorithm is proposed, together with graph invariants having a global nature.

Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement

An O((m+n)log n) algorithm is given for finding a canonical version of a stable colouring, on graphs with n vertices and m edges, which captures all known colour refinement algorithms.

Practical graph isomorphism, II

Engineering an Efficient Canonical Labeling Tool for Large and Sparse Graphs

Within the general framework of backtracking algorithms based on individualization and refinement, data structures, subroutines, and pruning heuristics especially for fast handling of large and sparse graphs are developed.

Fast Algorithm for Graph Isomorphism Testing

A novel approach to the graph isomorphism problem is presented, that tries to find a mapping between the two input graphs using backtracking, with a (possibly partial) automorphism precomputing that allows to prune the search tree.

Conflict Propagation and Component Recursion for Canonical Labeling

Two new search space pruning techniques, conflict propagation based on recorded failure information and recursion over nonuniformly joined components, are presented and Experimental results show that the techniques can result in substantial decrease in both search space sizes and run times.

Conauto-2.0: Fast Isomorphism Testing and Automorphism Group Computation

It is proved that, under some circumstances, it is not only possible to prune the search space, but also to infer new generators without the need of explicitly finding an automorphism of the graph.

Benchmark Graphs for Practical Graph Isomorphism

A construction to efficiently generate small instances for the graph isomorphism problem that are difficult or even infeasible for said solvers is described and it is possible to generate an abundance of instances of arbitrary size.

An optimal lower bound on the number of variables for graph identification

It is shown that Omega (n) variables are needed for first-order logic with counting to identify graphs on n vertices and the lower bound is optimal up to multiplication by a constant.

An Efficient Algorithm for Graph Isomorphism

It is shown that the re ordered graphs form a sufficiency condition for isomorphism; namely, if the reordered graphs are identical, then the given graphs are isomorphic.