New Results for Network Pollution Games

Abstract

We study a newly introduced network model of the pollution control and design approximation algorithms and truthful mechanisms with objective to maximize the social welfare. On a high level, we are given a graph whose nodes represent the agents (sources of pollution), and edges between agents represent the effect of pollution spread. The government is responsible to maximize the social welfare while setting bounds on the levels of emitted pollution both locally and globally. We obtain a truthful in expectation FPTAS when the network is a tree (modelling water pollution) and a deterministic truthful 3-approximation mechanism. On planar networks (modelling air pollution) the previous result was a huge constant approximation algorithm. We design a PTAS with a small violation of local pollution constraints. We also design approximation algorithms for general networks with bounded degree. Our approximations are near best possible under appropriate complexity assumptions.