Before revision: Given a compact E \subset R^n and s > 0, the maximum distance problem asks to find a compact and connected subset of R^n of smallest one dimensional Hausdorff measure , whose s-neighborhood covers E.
After revision: Given a compact E \subset R^n and s > 0, the maximum distance problem asks to find a compact and connected subset of R^n of smallest one dimensional Hausdorff measure whose s-neighborhood covers E.