Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems
arxiv(2024)
摘要
We consider the problem of finding a basis of a matroid with weight exactly
equal to a given target. Here weights can be discrete values from
{-Δ,…,Δ} or more generally m-dimensional vectors of such
discrete values. We resolve the parameterized complexity completely, by
presenting an FPT algorithm parameterized by Δ and m for arbitrary
matroids. Prior to our work, no such algorithms were known even when weights
are in {0,1}, or arbitrary Δ and m=1. Our main technical
contributions are new proximity and sensitivity bounds for matroid problems,
independent of the number of elements. These bounds imply FPT algorithms via
matroid intersection.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要