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In the restricted Santa Claus problem we are given resources $\mathcal R$ andplayers $\mathcal P$. Every resource $j\in\mathcal R$ has a value $v_j$ andevery player $i$ desires a set $\mathcal R(i)$ of resources. We are interestedin distributing the resources to players that desire them. The quality of asolution is measured by the least happy player, i.e., the lowest sum ofresource values. This value should be maximized. The local search algorithm byAsadpour et al. and its connection to the configuration LP has proved itself tobe a very influential technique for this and related problems. In the originalproof, a local search was used to obtain a bound of $4$ for the ratio of thefractional to the integral optimum of the configuration LP (integrality gap).This bound is non-constructive since the local search has not been shown toterminate in polynomial time. On the negative side, the worst instance knownhas an integrality gap of $2$. Although much progress was made in this area,neither bound has been improved since. We present a better analysis that showsthe integrality gap is not worse than $3 + 5/6 \approx 3.8333$.

A note on the integrality gap of the configuration LP for restricted Santa Claus