Object Migration Automata for Non-equal Partitioning Problems with Known Partition Sizes
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2021Metadata
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Omslandseter, R.O., Jiao, L., Oommen, B.J. (2021). Object Migration Automata for Non-equal Partitioning Problems with Known Partition Sizes. I: Maglogiannis, I., Macintyre, J., Iliadis, L. (red.) Artificial Intelligence Applications and Innovations. AIAI 2021. IFIP Advances in Information and Communication Technology, 627. Springer. https://doi.org/10.1007/978-3-030-79150-6_11Abstract
Solving partitioning problems in random environments is a classic and challenging task, and has numerous applications. The existing Object Migration Automaton (OMA) and its proposed enhancements, which include the Pursuit and Transitivity phenomena, can solve problems with equi-sized partitions. Currently, these solutions also include one where the partition sizes possess a Greatest Common Divisor (GCD). In this paper, we propose an OMA-based solution that can solve problems with both equally and non-equally-sized groups, without restrictions on their sizes. More specifically, our proposed approach, referred to as the Partition Size Required OMA (PSR-OMA), can solve general partitioning problems, with the only additional requirement being that the unconstrained partitions’ sizes are known a priori. The scheme is a fundamental contribution in the field of partitioning algorithms, and the numerical results presented demonstrate that PSR-OMA can solve both equi-partitioning and non-equi-partitioning problems efficiently, and is the only known solution that resolves this problem.