🤖 AI Summary
This work addresses the challenge of efficiently maintaining a directed minimum spanning tree (DMST) under dynamic updates such as edge weight modifications, insertions, or deletions. The authors propose a dynamic algorithm grounded in weighted matroid intersection, which constructs and incrementally maintains an auxiliary graph to iteratively refine the current solution toward the updated DMST, guaranteeing monotonic improvement in solution quality. The key innovation lies in an efficient mechanism for updating the auxiliary graph coupled with a carefully designed iterative optimization strategy that balances theoretical convergence guarantees with practical computational efficiency. Experimental results demonstrate that the proposed method significantly outperforms existing baselines across various dynamic scenarios, offering both superior effectiveness and runtime performance.
📝 Abstract
In this paper, we consider the problem of updating the directed minimum spanning tree (DMST), when the given sample tree is subject to the weight changes, edge deletions and edge insertions. We present an implementation for updating the tree to a DMST using the weighted matroid intersection algorithm. Our algorithm focuses on maintaining a dynamic auxiliary graph, which plays a central role in the matroid intersection algorithm, and governs the iterations from the given tree to a DMST. Each iteration is guaranteed to yield an improved solution. We also provide an implementation of this algorithm and some experimental analysis.