Before revision:  In addition, our dynamic version (that allows insertions and deletions of sites) also improves the space of Kaplan et al.'s recent SODA'17 work from O( n log^3 n ) to O( n log n ) , and reduces a ( log^2 n )-factor from their deletion time.
After revision:  In addition, our dynamic version (that allows insertions and deletions of sites) also reduces the space of Kaplan et al.'s recent SODA'17 work from O( n log^3 n ) to O( n log n ) , and reduces a ( log^2 n )-factor from their deletion time.