Hardness of Approximating Flow and Job Shop Scheduling Problems

Authors:
Monaldo Mastrolilli;Ola Svensson
Affiliations:
IDSIA, Lugano, Switzerland;EPFL, Switzerland
Venue:
Journal of the ACM (JACM)
Year:
2011

Citing 13
Cited 2

Improved Approximation Algorithms for Shop Scheduling Problems

SIAM Journal on Computing
Makespan minimization in preemptive two machine job shops

Computing
A new algorithm approach to the general Lovász local lemma with applications to scheduling and satisfiability problems (extended abstract)

STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Some APX-completeness results for cubic graphs

Theoretical Computer Science
Tighter bounds on preemptive job shop scheduling with two machines

Computing
Better Approximation Guarantees for Job-Shop Scheduling

SIAM Journal on Discrete Mathematics
Makespan Minimization in Job Shops: A Linear Time Approximation Scheme

SIAM Journal on Discrete Mathematics
Non-Approximability Results for Scheduling Problems with Minsum Criteria

INFORMS Journal on Computing
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring

FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Job Shop Scheduling with Unit Processing Times

Mathematics of Operations Research
Grouping Techniques for Scheduling Problems: Simpler and Faster

Algorithmica
Tight bounds for permutation flow shop scheduling

IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
An algorithmic approach to the lovász local lemma. I

Random Structures & Algorithms

A simpler proof for O(congestion+dilation) packet routing

IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
On the weak computability of a four dimensional orthogonal packing and time scheduling problem

Theoretical Computer Science

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Abstract

We consider several variants of the job shop problem that is a fundamental and classical problem in scheduling. The currently best approximation algorithms have worse than logarithmic performance guarantee, but the only previously known inapproximability result says that it is NP-hard to approximate job shops within a factor less than 5/4. Closing this big approximability gap is a well-known and long-standing open problem. This article closes many gaps in our understanding of the hardness of this problem and answers several open questions in the literature. It is shown the first nonconstant inapproximability result that almost matches the best-known approximation algorithm for acyclic job shops. The same bounds hold for the general version of flow shops, where jobs are not required to be processed on each machine. Similar inapproximability results are obtained when the objective is to minimize the sum of completion times. It is also shown that the problem with two machines and the preemptive variant with three machines have no PTAS.