Scheduling Tasks to Minimize Active Time on a Processor with Unlimited Capacity.

We study the following scheduling problem on a single processor. We are given n jobs, where each job j(i) has an integer release time r(i), processing time p(i) as well as deadline d(i). The processor can schedule an unlimited number of jobs at any time t. Our objective is to schedule the jobs together such that the total number of active time slots is minimized. We present an O(n(3)) dynamic programming algorithm for the case of agreeable deadlines with d(i) <= d(j) whenever r(i) < r(j) or all jobs are big. In the general case, we present an online algorithm with competitive ratio 4 and show that our analysis is tight.