Name
Abstract | ||
|---|---|---|
The General Scheduling Problem (GSP) generalizes scheduling problems with sum of cost objectives such as weighted flow time and weighted tardiness. Given a set of jobs with processing times, release dates, and job dependent cost functions, we seek to find a minimum cost preemptive schedule on a single machine. The best known algorithm for this problem and also for weighted flow time/tardiness is an O(loglog P)-approximation (where P denotes the range of the job processing times), while the best lower bound shows only strong NP-hardness. When release dates are identical there is also a gap: the problem remains strongly NP-hard and the best known approximation algorithm has a ratio of e+epsilon (running in quasi-polynomial time). reduce the latter gap by giving a QPTAS if the numbers in the input are quasi-polynomially bounded, ruling out the existence of an APX-hardness proof unless NPsubseteq DTIME(2^polylog(n)). Our techniques are based on the QPTAS known for the UFP-Cover problem, a particular case of GSP where we must pick a subset of intervals (jobs) on the real line with associated heights and costs. If an interval is selected, its height will help cover a given demand on any point contained within the interval. reduce our problem to a generalization of UFP-Cover and use a sophisticated divide-and-conquer procedure with interdependent non-symmetric subproblems. We also present a pseudo-polynomial time approximation scheme for two variants of UFP-Cover. For the case of agreeable intervals we give an algorithm based on a new dynamic programming approach which might be useful for other problems of this type. The second one is a resource augmentation setting where we are allowed to slightly enlarge each interval. |
Year | Venue | Field |
|---|---|---|
2017 | ICALP | Discrete mathematics,Dynamic programming,Approximation algorithm,DTIME,Combinatorics,Tardiness,Job shop scheduling,Scheduling (computing),Upper and lower bounds,Mathematics,Bounded function |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
0 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Antonios Antoniadis | 1 | 127 | 13.81 |
| Ruben Hoeksma | 2 | 33 | 8.23 |
| Julie Meißner | 3 | 0 | 0.34 |
| José Verschae | 4 | 133 | 13.23 |
| Andreas Wiese | 5 | 71 | 10.71 |