Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
A cutting plane algorithm for a clustering problem
Mathematical Programming: Series A and B
Facets of the clique partitioning polytope
Mathematical Programming: Series A and B
On the partial order polytope of a digraph
Mathematical Programming: Series A and B
Adjacency of vertices of the complete pre-order polytope
Discrete Mathematics
Combinatorial optimization
`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications
Journal of the ACM (JACM)
Performance evaluation of a parallel tabu search task scheduling algorithm
Parallel Computing - High performance computing in operations research
Operating Systems Theory
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Facets of the Weak Order Polytope Derived from the Induced Partition Projection
SIAM Journal on Discrete Mathematics
On Mapping Systolic Algorithms onto the Hypercube
IEEE Transactions on Parallel and Distributed Systems
Performance of Synchronous Parallel Algorithms with Regular Structures
IEEE Transactions on Parallel and Distributed Systems
Processor Assignment in Heterogeneous Parallel Architectures
IPPS '92 Proceedings of the 6th International Parallel Processing Symposium
The maximum common edge subgraph problem: A polyhedral investigation
Discrete Applied Mathematics
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We consider the problem of scheduling a set of tasks related by precedence constraints to a set of processors, so as to minimize their makespan. Each task has to be assigned to a unique processor and no preemption is allowed. A new integer programming formulation of the problem is given and strong valid inequalities are derived. A subset of the inequalities in this formulation has a strong combinatorial structure, which we use to define the polytope of partitions into linear orders. The facial structure of this polytope is investigated and facet defining inequalities are presented which may be helpful to tighten the integer programming formulation of other variants of multiprocessor scheduling problems. Numerical results on real-life problems are presented.