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arXiv · 2402.15485

Graph Partitioning With Limited Moves

Majid Behbahani·Mina Dalirrooyfard·Elaheh Fata·Yuriy Nevmyvaka
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Abstract

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.

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Majid Behbahani, Mina Dalirrooyfard, Elaheh Fata, Yuriy Nevmyvaka. 2024-02-23. Graph Partitioning With Limited Moves. https://arxiv.org/abs/2402.15485

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