Problems on group-labeled matroid bases

F Hörsch, A Imolay, R Mizutani, T Oki… - arxiv preprint arxiv …, 2024 - arxiv.org
Consider a matroid equipped with a labeling of its ground set to an abelian group. We define
the label of a subset of the ground set as the sum of the labels of its elements. We study a …

Survey of Results on the ModPath and ModCycle Problems

A Amarilli - arxiv preprint arxiv:2409.00770, 2024 - arxiv.org
This note summarizes the state of what is known about the tractability of the problem
ModPath, which asks if an input undirected graph contains a simple st-path whose length …

The complexity of regular trail and simple path queries on undirected graphs

W Martens, T Popp - Proceedings of the 41st ACM SIGMOD-SIGACT …, 2022 - dl.acm.org
We study the data complexity of regular trail and simple path queries on undirected graphs.
Using techniques from structural graph theory, ranging from the graph minor theorem to …

Towards the Proximity Conjecture on Group-Labeled Matroids

D Garamvölgyi, R Mizutani, T Oki, T Schwarcz… - arxiv preprint arxiv …, 2024 - arxiv.org
Consider a matroid $ M $ whose ground set is equipped with a labeling to an abelian group.
A basis of $ M $ is called $ F $-avoiding if the sum of the labels of its elements is not in a …

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 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 …

[PDF][PDF] 群ラベル付きグラフにおける組合せ最適化

山口勇太郎 - … リサーチ= Communications of the Operations Research …, 2021 - orsj.org
グラフにおける組合せ最適化は, アルゴリズムの理論に関する中心的な話題として, 20
世紀半ばから盛んに研究されてきた. 群ラベル付きグラフは, ネットワーク構造における偶奇性や …