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Algorithms on Discrete Near Optimal Partitions
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In practice, many NP-hard combinatorial optimization§ problems can be formulated as partitioning problems.§In such a formulation, each component in the§partition is assigned with a numerical objective§value and the objective function is defined as a§function on the numerical values assigned. The§optimization problem is to minimize or maximize §the objective function on all possible partitions§that satisfy certain constraints. A feasible§partition (i.e., a partition that satisfy all the§constraints) with the optimal objective value is§called an optimal partition. A near-optimal partition§is a partition with an objective value close to the§optimal value. In a partitioning problem, by§exploiting the properties of the underlying §domain, one may be able to construct efficient§heuristic algorithms to produce near-optimal§partitions. We present algorithms for applications in§Higher Dimensional Domain Decomposition, Intensity§Modulated Radiation Therapy (IMRT) including§Intensity Modulated Arc Therapy (IMAT)
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