ToTo: an open database for computation, storage and retrieval of tree decompositions. Many NP-hard problems on graphs become tractable on graphs of low treewidth, but the corresponding algorithms require access to a tree decomposition of the graph of low (ideally, minimum) width. Unfortunately computation of treewidth is itself NP-hard and a wide variety of exact, heuristic and approximation algorithms have been proposed for this problem. To support this ongoing research we present here {sc ToTo}, an open graph database for computation, storage and rapid retrieval of tree decompositions. We hope that the database will become both a central repository for important graphs and benchmark datasets and extend the use of treewidth beyond the usual communities: the database and associated algorithms can be accessed via a web browser and do not require installation of any specialist software.

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