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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