2 research outputs found
Graph Partitioning With Limited Moves
In many real world networks, there already exists a (not necessarily optimal)
-partitioning of the network. Oftentimes, one aims to find a
-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 -move
-partitioning~problem, a natural variant of the Multiway cut problem. Given
a graph, a set of terminals and an initial partitioning of the graph, the
-move -partitioning~problem aims to find a -partitioning with the
minimum-weighted cut among all the -partitionings that can be obtained by
moving at most non-terminal nodes to partitions different from their
initial ones. Our main result is a polynomial time approximation
algorithm for this problem. We further show that this problem is -hard,
and give an FPTAS for when is a small constant.Comment: shortened version accepted in AISTATS 2024 as ora