Scalable generalized median graph estimation and its manifold use in bioinformatics, clustering, classification, and indexing

In this paper, we present GMG-BCU — a local search algorithm based on block coordinate update for estimating generalized median graph given collection of labeled or unlabeled input graphs. Unlike all competitors, is designed both discrete and continuous label spaces can be configured to run in linear time w. r. t. the size whenever node edge labels are computable time. These properties make usable applications such as differential microbiome data analysis, classification, clustering, indexing. We also prove theoretical graphs, namely, that they exist under reasonable assumptions which met almost application scenarios, general non-unique, NP-hard compute APX-hard approximate, no polynomial ?-approximation exists any ? unless isomorphism problem P. Extensive experiments six different datasets show our heuristic always outperforms state art terms runtime quality (on most datasets, quality), it only available cope with collections containing several thousands shows very promising potential when used aforementioned applications. freely GitHub: https://github.com/dbblumenthal/gedlib/.