Lasserre Hierarchy for Graph Isomorphism and Homomorphism Indistinguishability
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We show that feasibility of the tth level of the Lasserre semidefinite programming hierarchy for graph isomorphism can be expressed as a homomorphism indistinguishability relation. In other words, we define a class Lt of graphs such that graphs G and H are not distinguished by the tth level of the Lasserre hierarchy if and only if they admit the same number of homomorphisms from any graph in Lt. By analysing the treewidth of graphs in Lt we prove that the 3tth level of Sherali–Adams linear programming hierarchy is as strong as the tth level of Lasserre. Moreover, we show that this is best possible in the sense that 3t cannot be lowered to 3t − 1 for any t. The same result holds for the Lasserre hierarchy with non-negativity constraints, which we similarly characterise in terms of homomorphism indistinguishability over a family L+t of graphs. Additionally, we give characterisations of level-t Lasserre with non-negativity constraints in terms of logical equivalence and via a graph colouring algorithm akin to the Weisfeiler–Leman algorithm. This provides a polynomial time algorithm for determining if two given graphs are distinguished by the tth level of the Lasserre hierarchy with non-negativity constraints.
Originalsprog | Engelsk |
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Titel | 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023 |
Redaktører | Kousha Etessami, Uriel Feige, Gabriele Puppis |
Antal sider | 18 |
Forlag | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Publikationsdato | 2023 |
Artikelnummer | 101 |
ISBN (Elektronisk) | 9783959772785 |
DOI | |
Status | Udgivet - 2023 |
Begivenhed | 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023 - Paderborn, Tyskland Varighed: 10 jul. 2023 → 14 jul. 2023 |
Konference
Konference | 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023 |
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Land | Tyskland |
By | Paderborn |
Periode | 10/07/2023 → 14/07/2023 |
Sponsor | DeepL, et al., Paderborn Center for Parallel Computing (PC2), REPLY, SFB 901, Stiebel Eltron |
Navn | Leibniz International Proceedings in Informatics, LIPIcs |
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Vol/bind | 261 |
ISSN | 1868-8969 |
Bibliografisk note
Funding Information:
Funding David E. Roberson: Supported by the Carlsberg Foundation Young Researcher Fellowship CF21-0682 – “Quantum Graph Theory”. Tim Seppelt: German Research Council (DFG) within Research Training Group 2236 (UnRAVeL) Acknowledgements Initial discussions for this work took place at Dagstuhl Seminar 22051 “Finite and Algorithmic Model Theory”.
Funding Information:
David E. Roberson: Supported by the Carlsberg Foundation Young Researcher Fellowship CF21-0682 – “Quantum Graph Theory”. Tim Seppelt: German Research Council (DFG) within Research Training Group 2236 (UnRAVeL)
Publisher Copyright:
© David E. Roberson and Tim Seppelt.
ID: 362936480