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Relational consistency algorithms and their application in finding subgraph and graph isomorphisms

Classics

The determination of subgraph and graph isomorphisms is an important application for the algebraic manipulation of networks of binary constraints. Simplified and streamlined arc consistency and tree search algorithms are introduced, and experimental results show substantial reduction in timings compared with previous algorithms for determining isomorphisms. Several path consistency algorithms, including a new one, have been timed experimentally on isomorphism problems, and found not to be cost effective despite their theoretical appeal. The importance of this result is enhanced by the absence of previously published experimentation with path consistency. A theoretical study of the new path consistency algorithm provides insight into the experimental results.


Universal Function Approximation on Graphs using Multivalued Functions

arXiv.org Machine Learning

In this work we produce a framework for constructing universal function approximators on graph isomorphism classes. Additionally, we prove how this framework comes with a collection of theoretically desirable properties and enables novel analysis. We show how this allows us to outperform state of the art on four different well known datasets in graph classification and how our method can separate classes of graphs that other graph-learning methods cannot. Our approach is inspired by persistence homology, dependency parsing for Natural Language Processing, and multivalued functions. The complexity of the underlying algorithm is O(mn) and code is publicly available.


A Necessary and Sufficient Condition for Graph Matching Being Equivalent to the Maximum Weight Clique Problem

arXiv.org Artificial Intelligence

This paper formulates a necessary and sufficient condition for a generic graph matching problem to be equivalent to the maximum vertex and edge weight clique problem in a derived association graph. The consequences of this results are threefold: first, the condition is general enough to cover a broad range of practical graph matching problems; second, a proof to establish equivalence between graph matching and clique search reduces to showing that a given graph matching problem satisfies the proposed condition; and third, the result sets the scene for generic continuous solutions for a broad range of graph matching problems. To illustrate the mathematical framework, we apply it to a number of graph matching problems, including the problem of determining the graph edit distance.


A Fast and Optimal Hand Isomorphism Algorithm

AAAI Conferences

In a section of their 2007 paper, Gilpen et. al. outline a technique for indexing poker hands that accounts for suit isomorphisms. Their implementation is specific to Texas Hold'em as it requires a large case analysis, and is not optimal as many cases are omitted. In this paper, we build on their ideas and provide a fast and optimal technique that generalizes beyond Texas Hold'em as well as provide an inverse mapping from an index to a canonical hand.


cgSpan: Closed Graph-Based Substructure Pattern Mining

arXiv.org Artificial Intelligence

For the same purpose, ClosedGraph must examine extensions from all vertices. The goal of Frequent Subgraph Mining (FSM) is to find (ii) cgSpan uses an efficient look-up table to check if early subgraphs in a given labeled graphs set that occur more termination can be applied to the graph. Only a single frequently than a given value. This value, known as support, lookup of the edge projections set of the last DFS code is usually expressed as a percentage of the set size. FSM of the graph is required. After the lookup, the equivalent algorithms can be designed to produce two types of output.