2024/09/11 by Guo, Heng, N, Vishvajeet · 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.2409.07283
We give a deterministic polynomial-time approximation scheme (FPTAS) for the volume of the truncated fractional matching polytope for graphs of maximum degree Δ, where the truncation is by restricting each variable to the interval [0,\frac1+δΔ], and δ≤ \fracCΔ for some constant C>0. We also generalise our result to the fractional matching polytope for hypergraphs of maximum degree Δ and maximum hyperedge size k, truncated by [0,\frac1+δΔ] as well, where δ≤ CΔ-(2k-3)/(k-1)k-1 for some constant C>0. The latter result generalises both the first result for graphs (when k=2), and a result by Bencs and Regts (2024) for the truncated independence polytope (when Δ=2). Our approach is based on the cluster expansion technique.