2022/03/09 by Majewski, Konrad, Masařík, Tomáš, Novotná, Jana +4 · 1 citation
#Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2203.04836
We revisit recent developments for the Maximum Weight Independent Set problem in graphs excluding a subdivided claw St,t,t as an induced subgraph [Chudnovsky, Pilipczuk, Pilipczuk, Thomassé, SODA 2020] and provide a subexponential-time algorithm with improved running time 2O(√(n)log n) and a quasipolynomial-time approximation scheme with improved running time 2^O(ε-1 log5 n). The Gyárfás' path argument, a powerful tool that is the main building block for many algorithms in Pt-free graphs, ensures that given an n-vertex Pt-free graph, in polynomial time we can find a set P of at most t-1 vertices, such that every connected component of G-N[P] has at most n/2 vertices. Our main technical contribution is an analog of this result for St,t,t-free graphs: given an n-vertex St,t,t-free graph, in polynomial time we can find a set P of O(t log n) vertices and an extended strip decomposition (an appropriate analog of the decomposition into connected components) of G-N[P] such that every particle (an appropriate analog of a connected component to recurse on) of the said extended strip decomposition has at most n/2 vertices.