Year: 2016
Type: preprint
Abstract: We consider the following single-machine scheduling problem, which is often denoted $1||\sum f_{j}$: we are given $n$ jobs to be scheduled on a single machine, where each job $j$ has an integral processing time $p_j$, and there is a nondecreasing, nonnegative cost function $f_j(C_{j})$ that specifies the cost of finishing $j$ at time $C_{j}$; the objective is to minimize $\sum_{j=1}^n f_j(C_j)$. Bansal \& Pruhs recently gave the first constant approximation algorithm with a performance guarantee of 16. We improve on this result by giving a primal-dual pseudo-polynomial-time algorithm based on the recently introduced knapsack-cover inequalities. The algorithm finds a schedule of cost at most four times the constructed dual solution. Although we show that this bound is tight for our algorithm, we leave open the question of whether the integrality gap of the LP is less than 4. Finally, we show how the technique can be adapted to yield, for any $ε>0$, a $(4+ε)$-approximation algorithm for this problem.
Source: arXiv (Cornell University)
Language: English
Subfield: Industrial and Manufacturing Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: AF: Small: Approximation Algorithms for Problems in Logistics, AF: Small: AAdvances in the Design of Approximation Algorithms for Optimization Problems, Collaborative Research: CompSustNet: Expanding the Horizons of Computational Sustainability, G6573591111, Collaborative Research: Computational Sustainability: Computational Methods for a Sustainable Environment, Economy, and Society
OpenAlex ID: W2951661752