Lower-complexity algorithms for fixed node search in multi-leader DAGs

Develop efficient algorithms with lower worst-case time complexity than the proposed labeling-based fixed node search (Algorithm 1) for determining fixed nodes in p-layered directed acyclic graphs, particularly in the multi-leader case (m ≥ 2) where the underlying m-vertex disjoint paths problem renders the approach NP-hard and computationally expensive on large-scale networks.

Background

The paper proposes an algorithm that simultaneously labels layers and determines fixed nodes in DAGs, leveraging reductions to m-vertex disjoint paths problems. The authors analyze complexity: for m ≥ 2, the problem becomes NP-hard, leading to high computational costs, especially for large networks.

Given this complexity barrier, the authors explicitly indicate the need for improved algorithms with lower time complexity that remain effective on complex graphs and large-scale instances.