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I know that it has been conjectured that the Gilmore–Gomory LP for 1-D BP (also known as configuration LP) has Modified Integer Roundup Property, i.e., Opt ≤ ⌈Opt_f⌉ + 1. However, I could not find the best-known lower bound for the integrality gap of the latter LP. Can anyone refer me to such a result?

Thanks in advance.

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