Known results deg≤d+l ☑deg≤k+l C2 independent sets of hypergraphs of max-degree≤d+1 and max-edge-size≤k+l C4 cs partition function: Z= 入川1 元∈{0,1}n satisfying Boolean at-most-1 all constraints variables constraints Classification of approximability in terms of )d,k? ●k=l:hardcore model d=1:monomer-dimer model ●forλ=1： [Dudek,Karpinski,Rucinski,Szymanska 2014]:FPTAS when d=2,k<2 [Liu and Lu 2015]FPTAS when d=2,k<3Known results • k=1: hardcore model • d=1: monomer-dimer model •for λ=1: •[Dudek, Karpinski, Rucinski, Szymanska 2014]: FPTAS when d=2, k≤2 •[Liu and Lu 2015] FPTAS when d=2, k≤3 Boolean variables deg ≤ d+1 deg ≤ k+1 x1 x2 x3 x4 x5 c1 c2 c3 c4 c5 c6 c7 at-most-1 constraints Z = X ~x2{0,1}n satisfying all constraints ￾k~ xk1 partition function: independent sets of hypergraphs of max-degree ≤ d+1 and max-edge-size ≤ k+1 Classification of approximability in terms of λ, d, k ?