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- W4383465335 abstract "We show that feasibility of the $t^text{th}$ 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 $mathcal{L}_t$ of graphs such that graphs $G$ and $H$ are not distinguished by the $t^text{th}$ level of the Lasserre hierarchy if and only if they admit the same number of homomorphisms from any graph in $mathcal{L}_t$. By analysing the treewidth of graphs in $mathcal{L}_t$ we prove that the $3t^text{th}$ level of Sherali--Adams linear programming hierarchy is as strong as the $t^text{th}$ 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 $mathcal{L}_t^+$ 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 $t^text{th}$ level of the Lasserre hierarchy with non-negativity constraints." @default.
- W4383465335 created "2023-07-07" @default.
- W4383465335 creator A5023984902 @default.
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- W4383465335 date "2023-02-21" @default.
- W4383465335 modified "2023-10-16" @default.
- W4383465335 title "Lasserre Hierarchy for Graph Isomorphism and Homomorphism Indistinguishability" @default.
- W4383465335 doi "https://doi.org/10.4230/lipics.icalp.2023.101" @default.
- W4383465335 hasPublicationYear "2023" @default.
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