Local approximation algorithms for a class of 0/1 max-min linear programs

We study the applicability of distributed, local algorithms to 0/1 max-min LPs where the objective is to maximise mink P v ckvxv subject to P v aivxv ≤ 1 for each i and xv ≥ 0 for each v. Here ckv ∈ {0, 1}, aiv ∈ {0, 1}, and the support sets Vi = {v : aiv > 0} and Vk = {v : ckv > 0} have bounded size; in particular, we study the case |Vk| ≤ 2. Each agent v is responsible for choosing the value of xv based on information within its constant-size neighbourhood; the communication network is the hypergraph where the sets Vk and Vi constitute the hyperedges. We present a local approximation algorithm which achieves an approximation ratio arbitrarily close to the theoretical lower bound presented in prior work.