Single and multiple device DSA problems, complexities and online algorithms

We study the single-device Dynamic Storage Allocation (DSA) problem and the multi-device Balancing DSA problem in this paper. The goal is to dynamically allocate the job into memory to minimize the usage of space without concurrency. The SRF problem is just a variant of the DSA problem. Our results are as follows.
• The NP-completeness for the 2-SRF problem, 3-DSA problem, and DSA problem for jobs with agreeable deadlines.
• An improved 3-competitive algorithm for jobs with agreeable deadlines on single-device DSA problems. A 4-competitive algorithm for jobs with agreeable deadlines on multi-device Balancing DSA problems.
• Lower bounds for jobs with agreeable deadlines: any non-clairvoyant algorithm cannot be (2−ϵ)-competitive and any clairvoyant algorithm cannot be (1.54−ϵ)-competitive.
• The first O(logL)-competitive algorithm for general jobs on multi-device Balancing DSA problems without any assumption.