Papers › Interdiction of minimum spanning trees and other matroid bases
Interdiction of minimum spanning trees and other matroid bases
Noah Weninger, Ricardo Fukasawa
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
In the minimum spanning tree (MST) interdiction problem, we are given a graph G=(V,E) with edge weights, and want to find some X⊆E satisfying a knapsack constraint such that the MST weight in (V,E∖X) is maximized. Since MSTs of G are the minimum weight bases in the graphic matroid of G, this problem is a special case of matroid interdiction on a matroid M=(E,ℐ), in which the objective is instead to maximize the minimum weight of a basis of M which is disjoint from X. By reduction from 0-1 knapsack, matroid interdiction is NP-complete, even for uniform matroids. We develop a new exact algorithm to solve the matroid interdiction problem. One of the key components of our algorithm is a dynamic programming upper bound which only requires that a simpler discrete derivative problem can be calculated/approximated for the given matroid. Our exact algorithm then uses this bound within a custom branch-and-bound algorithm. For different matroids, we show how this discrete derivative can be calculated/approximated. In particular, for partition matroids, this yields a pseudopolynomial time algorithm. For graphic matroids, an approximation can be obtained by solving a sequence of minimum cut problems, which we apply to the MST interdiction problem. The running time of our algorithm is asymptotically faster than the best known MST interdiction algorithm, up to polylog factors. Furthermore, our algorithm achieves state-of-the-art computational performance: we solved all available instances from the literature, and in many cases reduced the best running time from hours to seconds.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections