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A Note on Edge-based Graph Partitioning and its Linear Algebraic Structure

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Journal of Mathematical Modelling and Algorithms

Abstract

We analyze two essential problems arising from edge-based graph partitioning. We show that one of them is an NP-hard problem but the other is in P, presenting a novel methodology that links linear algebra theory to the graph problems as a part of proving the facts. This is a significant trial in that linear algebra, which has been mostly adopted as a theoretical analysis tool, is practically applied to solving actual graph problems. As a result of the linear algebraic manipulation, we could devise a linear-time algorithm for the problem in P.

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Authors and Affiliations

  1. School of Computer Science & Engineering, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul, 151-744, Korea

    Yourim Yoon & Byung-Ro Moon

  2. Department of Computer Science & Engineering, Kwangwoon University, 20 Kwangwoon-ro, Nowon-gu, Seoul, 139-701, Korea

    Yong-Hyuk Kim

Authors
  1. Yourim Yoon
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  2. Yong-Hyuk Kim
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  3. Byung-Ro Moon
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Correspondence to Byung-Ro Moon.

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Yoon, Y., Kim, YH. & Moon, BR. A Note on Edge-based Graph Partitioning and its Linear Algebraic Structure. J Math Model Algor 10, 269–276 (2011). https://doi.org/10.1007/s10852-011-9154-4

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  • DOI: https://doi.org/10.1007/s10852-011-9154-4

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