Lasserre Hierarchy for Graph Isomorphism and Homomorphism Indistinguishability
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Documents
- Fulltext
Final published version, 893 KB, PDF document
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.
Original language | English |
---|---|
Title of host publication | 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023 |
Editors | Kousha Etessami, Uriel Feige, Gabriele Puppis |
Number of pages | 18 |
Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Publication date | 2023 |
Article number | 101 |
ISBN (Electronic) | 9783959772785 |
DOIs | |
Publication status | Published - 2023 |
Event | 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023 - Paderborn, Germany Duration: 10 Jul 2023 → 14 Jul 2023 |
Conference
Conference | 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023 |
---|---|
Land | Germany |
By | Paderborn |
Periode | 10/07/2023 → 14/07/2023 |
Sponsor | DeepL, et al., Paderborn Center for Parallel Computing (PC2), REPLY, SFB 901, Stiebel Eltron |
Series | Leibniz International Proceedings in Informatics, LIPIcs |
---|---|
Volume | 261 |
ISSN | 1868-8969 |
Bibliographical note
Publisher Copyright:
© David E. Roberson and Tim Seppelt.
- graph isomorphism, homomorphism indistinguishability, Lasserre hierarchy, linear programming, semidefinite programming, Sherali–Adams hierarchy, treewidth
Research areas
ID: 362936480