An improved approximation algorithm for scheduling monotonic moldable tasks

We are concerned with the problem of scheduling monotonic moldable tasks on identical processors to minimize makespan. focus natural case where number m as resources is fixed or relatively small compared n tasks. present an efficient (3/2)-approximation algorithm time complexity O(nmlog(nm)) (for m>n) and O(n2logn) m?n). To best our knowledge, relevant known results are: (a) a (3/2+?)-approximation O(nmlog(n/?)), (b) fully polynomial-time approximation scheme for m?16n/?, (c) O(ng(1/?)) when bounded by polynomial in n, g(·) super-exponential function. On other hand, novel general technique developed this paper removing ?-term worst-case performance ratio can be applied improving guarantee certain dual algorithms combinatorial optimization problems.