# Improved local search for graph edit distance

## TL;DR

This paper introduces two novel local search algorithms, K-REFINE and RANDPOST, that improve the approximation of graph edit distance, especially on small and large graphs respectively, through enhanced heuristics and stochastic warm starts.

## Contribution

The paper presents K-REFINE, an improved local search algorithm, and RANDPOST, a stochastic warm start framework, advancing approximate GED computation methods.

## Key findings

- K-REFINE outperforms existing local search algorithms on small graphs.
- RANDPOST efficiently generates promising initial solutions for large graphs.
- Both methods demonstrate strong empirical performance in practice.

## Abstract

The graph edit distance (GED) measures the dissimilarity between two graphs as the minimal cost of a sequence of elementary operations transforming one graph into another. This measure is fundamental in many areas such as structural pattern recognition or classification. However, exactly computing GED is NP-hard. Among different classes of heuristic algorithms that were proposed to compute approximate solutions, local search based algorithms provide the tightest upper bounds for GED. In this paper, we present K-REFINE and RANDPOST. K-REFINE generalizes and improves an existing local search algorithm and performs particularly well on small graphs. RANDPOST is a general warm start framework that stochastically generates promising initial solutions to be used by any local search based GED algorithm. It is particularly efficient on large graphs. An extensive empirical evaluation demonstrates that both K-REFINE and RANDPOST perform excellently in practice.

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Source: https://tomesphere.com/paper/1907.02929