Graph Partitioning With Limited Moves
<|reference_start|>Graph Partitioning With Limited Moves: In many real world networks, there already exists a (not necessarily optimal) $k$-partitioning of the network. Oftentimes, one aims to find a $k$-partitioning with a smaller cut value for such networks by moving only a few nodes across partitions. The number of nodes that can be moved across partitions is often a constraint forced by budgetary limitations. Motivated by such real-world applications, we introduce and study the $r$-move $k$-partitioning~problem, a natural variant of the Multiway cut problem. Given a graph, a set of $k$ terminals and an initial partitioning of the graph, the $r$-move $k$-partitioning~problem aims to find a $k$-partitioning with the minimum-weighted cut among all the $k$-partitionings that can be obtained by moving at most $r$ non-terminal nodes to partitions different from their initial ones. Our main result is a polynomial time $3(r+1)$ approximation algorithm for this problem. We further show that this problem is $W[1]$-hard, and give an FPTAS for when $r$ is a small constant.<|reference_end|>
@article{behbahani2024graph,
    title={Graph Partitioning With Limited Moves},
    author={Majid Behbahani, Mina Dalirrooyfard, Elaheh Fata, Yuriy Nevmyvaka},
    journal={arXiv preprint arXiv:2402.15485},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.15485},
    primaryClass={cs.DS}
}