Graphs and algorithms
Fast algorithms for convex quadratic programming and multicommodity flows
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Combinatorial algorithms for the generalized circulation problem
Mathematics of Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Polynomial-time highest-gain augmenting path algorithms for the generalized circulation problem
Mathematics of Operations Research
Faster Algorithms for the Generalized Network Flow Problem
Mathematics of Operations Research
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Improved Approximation Schemes for Scheduling Unrelated Parallel Machines
Mathematics of Operations Research
Approximation Algorithms for Single-Source Unsplittable Flow
SIAM Journal on Computing
Scheduling Tasks on Unrelated Machines: Large Neighborhood Improvement Procedures
Journal of Heuristics
Single-source unsplittable flow
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Improving time bounds on maximum generalised flow computations by contracting the network
Theoretical Computer Science - Special issue on automata, languages and programming
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Speeding-up linear programming using fast matrix multiplication
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Scheduling unrelated parallel machines computational results
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
A survey of pipelined workflow scheduling: Models and algorithms
ACM Computing Surveys (CSUR)
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We consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption. Job i takes processing time pij on machine j, and the total time used by a machine is the sum of the processing times for the jobs assigned to it. The objective is to minimize makespan. The best known approximation algorithms for this problem compute an optimum fractional solution and then use rounding techniques to get an integral 2-approximation. In this paper we present a combinatorial approximation algorithm that matches this approximation quality. It is much simpler than the previously known algorithms and its running time is better. This is the first time that a combinatorial algorithm always beats the interior point approach for this problem. Our algorithm is a generic minimum cost flow algorithm, without any complex enhancements, tailored to handle unsplittable flow. It pushes unsplittable jobs through a two-layered bipartite generalized network defined by the scheduling problem. In our analysis, we take advantage from addressing the approximation problem directly. In particular, we replace the classical technique of solving the LP-relaxation and rounding afterwards by a completely integral approach. We feel that this approach will be helpful also for other applications.