Algorithms for minclique scheduling problems
Discrete Applied Mathematics - Special issue on models and algorithms for planning and scheduling problems
Mathematics of Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Molecular Solution to the Three-Partition Problem
Journal of Information Technology Research
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This note presents a generic approach to proving NP-hardness of unconstrained partition type problems, namely partitioning a given set of entities into several subsets such that a certain objective function of the partition is optimized. The idea is to represent the objective function of the problem as a function of aggregate variables, whose optimum is achieved only at the points where problem Partition (if proving ordinary NP-hardness), or problem 3-Partition or Product Partition (if proving strong NP-hardness) has a solution. The approach is demonstrated on a number of discrete optimization and scheduling problems.