A Flow-Based Method for Improving the Expansion or Conductance of Graph Cuts

We discuss the Max-flow Quotient-cut Improvement (MQI) algorithm, a flow-based method for improving graph cuts when cut quality is measured by quotient-style metrics such as expansion or conductance. Given a cut \((S,\overline{S})\), this algorithm finds the best improvement among all cuts \((S',\overline{S'})\) such that S′ is a strict subset of S. This idea has already been used by theorists to give improved bounds for graph bisection and for finding hierarchical oblivous routing schemes. Here we investigate the practical utility of the idea and find that MQI can be combined with Metis to obtain a heuristic graph partitioner that does an extremely good job on classic benchmark graphs, VLSI circuits, and four different tasks from the Information Retrieval domain. We also find empirically that Metis+MQI runs in nearly linear time, so it is applicable to very large problems.

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