The integrality gap of weighted $k$-matroid intersection

Partial on the headline conjecture, complete on a named part of another. For weighted $k$-matroid intersection the integrality gap is at most $k - 1 + 1/k$, improving the previous general bound of $k$ but not reaching the conjectured $k-1$. For weighted $p$-matchoids the gap is at most $p - 1 + 1/p$, with a deterministic LP-relative algorithm achieving the same factor; the paper states that this resolves the $p$-matchoid part of Lee, Sviridenko and Vondrák's Conjecture 1, and projective planes of order $p-1$ give tight instances whenever one exists.

Partial on the headline conjecture, complete on a named part of another. For weighted $k$-matroid intersection the integrality gap is at most $k - 1 + 1/k$, improving the previous general bound of $k$ but not reaching the conjectured $k-1$. For weighted $p$-matchoids the gap is at most $p - 1 + 1/p$, with a deterministic LP-relative algorithm achieving the same factor; the paper states that this resolves the $p$-matchoid part of Lee, Sviridenko and Vondrák's Conjecture 1, and projective planes of order $p-1$ give tight instances whenever one exists.