Solving Linear-Time FPT Problems with Interesting Connections

0/1/all CSPs, Half-Integral $A$-path Packing, and Linear-Time FPT Algorithms

In this paper, we address this issue by providing an algorithm for solving the half-integral optimal relaxation functions (lp) arising from various free-path (fp) problems, where is the optimalvalue and is the number of edges/constraints.The obtained running time for each of these problems is linear in the inputsize and has the current smallest dependency on the parameter.In particular, these algorithms are the first linear-time fpt algorithms for problems including group feedback vertex set and non-monochromatic cycle transversal.