Before revision:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O  n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K)   . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
After revision:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K)  . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).