2019/11/30 by Bosman, Thomas, Olver, Neil · 1 citation
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1912.00101
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of N items and a discrete time horizon of T days in which given demands for the items must be satisfied. Ordering a set of items incurs a cost according to a set function, with properties depending on the problem under consideration. Demand for an item at time t can be satisfied by an order on any day prior to t, but a holding cost is charged for storing the items during the intermediate period; the goal is to minimize the sum of the ordering and holding cost. Our approximation factor for both problems is O(log log min(N,T)); this improves exponentially on the previous best results.