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In this paper, we propose a new problem called the Maximum cardinality Acyclic Subset of Edges that Meets the Potential Requirements (MASEMPR). This problem abstracts several problems in logistics. Our focus is on a particular logistics problem called the Maximum Path Set (MPS) problem. We show that the MASEMPR problem is NP-hard. We then propose an exact exponential algorithm for the MASEMPR problem in subcubic graphs (graphs in which each vertex has degree at most 3). Finally, we design a constant factor approximation algorithm for the MASEMPR problem in general graphs.

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The MASEMPR Problem and Its Applications in Logistics

  • 会议论文

  • 发表日期：

    2025年

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  • A. Subramani,
  • K. Subramani,
  • Piotr Wojciechowski,
  • Sangram K. Jena

摘要

In this paper, we propose a new problem called the Maximum cardinality Acyclic Subset of Edges that Meets the Potential Requirements (MASEMPR). This problem abstracts several problems in logistics. Our focus is on a particular logistics problem called the Maximum Path Set (MPS) problem. We show that the MASEMPR problem is NP-hard. We then propose an exact exponential algorithm for the MASEMPR problem in subcubic graphs (graphs in which each vertex has degree at most 3). Finally, we design a constant factor approximation algorithm for the MASEMPR problem in general graphs.