Probabilistic analysis of algorithms: on computing methodologies for computer algorithms performance evaluation
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Structure of a simple scheduling polyhedron
Mathematical Programming: Series A and B
New results in the worst-case analysis for flow-shop scheduling
Discrete Applied Mathematics
Improved Approximation Algorithms for Shop Scheduling Problems
SIAM Journal on Computing
On some geometric methods in scheduling theory: a survey
Discrete Applied Mathematics
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Improved bounds for acyclic job shop scheduling (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Scheduling to minimize average completion time: off-line and on-line algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Makespan Minimization in Job Shops: A Linear Time Approximation Scheme
SIAM Journal on Discrete Mathematics
Improved Scheduling Algorithms for Minsum Criteria
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Improved Bounds for Flow Shop Scheduling
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Hardness of Approximating Flow and Job Shop Scheduling Problems
Journal of the ACM (JACM)
A linear time approximation algorithm for permutation flow shop scheduling
Theoretical Computer Science
Improved approximation algorithms for routing shop scheduling
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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In flow shop scheduling there are m machines and n jobs, such that every job has to be processed on the machines in the fixed order 1, . . ., m. In the permutation flow shop problem, it is also required that each machine processes the set of all jobs in the same order. Formally, given n jobs along with their processing times on each machine, the goal is to compute a single permutation of the jobs σ : [n] → [n], that minimizes the maximum job completion time (makespan) of the schedule resulting from σ. The previously best known approximation guarantee for this problem was O(√mlogm) [29]. In this paper, we obtain an improved O(min{√m, √n}) approximation algorithm for the permutation flow shop scheduling problem, by finding a connection between the scheduling problem and the longest increasing subsequence problem. Our approximation ratio is relative to the lower bounds of maximum job length and maximum machine load, and is the best possible such result. This also resolves an open question from [21], by algorithmically matching the gap between permutation and non-permutation schedules. We also consider the weighted completion time objective for the permutation flow shop scheduling problem. Using a natural linear programming relaxation, and our algorithm for the makespan objective, we obtain an O(min{√m, √n}) approximation algorithm for minimizing the total weighted completion time, improving upon the previously best known guarantee of Ɛm for any constant Ɛ 0 [30]. We give a matching lower bound on the integrality gap of our linear programming relaxation.