Faster algorithms on linear delta-matroids

T Koana, M Wahlström - arxiv preprint arxiv:2402.11596, 2024 - arxiv.org
We show new algorithms and constructions over linear delta-matroids. We observe an
alternative representation for linear delta-matroids, as a contraction representation over a …

A weighted linear matroid parity algorithm

S Iwata, Y Kobayashi - Proceedings of the 49th Annual ACM SIGACT …, 2017 - dl.acm.org
The matroid parity (or matroid matching) problem, introduced as a common generalization of
matching and matroid intersection problems, is so general that it requires an exponential …

Packing -Paths in Group-Labelled Graphs via Linear Matroid Parity

Y Yamaguchi - SIAM Journal on Discrete Mathematics, 2016 - SIAM
Mader's disjoint \calS-paths problem is a common generalization of non-bipartite matching
and Menger's disjoint paths problems. Lovász J. Combin. Theory Ser. B, 28 (1980), pp. 208 …

A Faster Deterministic Algorithm for Mader's -Path Packing

S Iwata, H Kinoshita - arxiv preprint arxiv:2411.18292, 2024 - arxiv.org
Given an undirected graph $ G=(V, E) $ with a set of terminals $ T\subseteq V $ partitioned
into a family $\mathcal {S} $ of disjoint blocks, find the maximum number of vertex-disjoint …

Finding a path with two labels forbidden in group-labeled graphs

Y Kawase, Y Kobayashi, Y Yamaguchi - Journal of Combinatorial Theory …, 2020 - Elsevier
The parity of the length of paths and cycles is a classical and well-studied topic in graph
theory and theoretical computer science. The parity constraints can be extended to label …

Shortest disjoint S-paths via weighted linear matroid parity

Y Yamaguchi - 27th International Symposium on Algorithms and …, 2016 - drops.dagstuhl.de
Mader's disjoint S-paths problem unifies two generalizations of bipartite matching:(a) non-
bipartite matching and (b) disjoint s–t paths. Lovász (1980, 1981) first proposed an efficient …

Finding a shortest non-zero path in group-labeled graphs

Y Iwata, Y Yamaguchi - Combinatorica, 2022 - Springer
We study a constrained shortest path problem in group-labeled graphs with nonnegative
edge length, called the shortest non-zero path problem. Depending on the group in …

A Blossom Algorithm for Maximum Edge-Disjoint T-Paths

S Iwata, Y Yokoi - Proceedings of the Fourteenth Annual ACM-SIAM …, 2020 - SIAM
Let G=(V, E) be a multigraph with a set T⊆ V of terminals. A path in G is called a T-path if its
ends are distinct vertices in T and no internal vertices belong to T. In 1978, Mader showed a …

A strongly polynomial algorithm for finding a shortest non-zero path in group-labeled graphs

Y Yamaguchi - Proceedings of the Fourteenth Annual ACM-SIAM …, 2020 - SIAM
We study a constrained shortest path problem in group-labeled graphs with nonnegative
edge length, called the shortest non-zero path problem. Depending on the group in …

Finding a path in group-labeled graphs with two labels forbidden

Y Kawase, Y Kobayashi, Y Yamaguchi - International Colloquium on …, 2015 - Springer
The parity of the length of paths and cycles is a classical and well-studied topic in graph
theory and theoretical computer science. The parity constraints can be extended to the label …