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.
X. Deng was supported by the National Science Foundation of China (Grant No. 61173011) and a Project 985 grant of Shanghai Jiaotong University. P. Krysta and J. Zhang were supported by the Engineering and Physical Sciences Research Council under grant EP/K01000X/1. M. Li was partly supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 117913). H. Qiao was supported by the National Science Foundation of China (Grant No. 71373262).
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Notes
- 1.
[15] uses cost function rather than benefit function, viewed as \(M_v-b_v(x_v)\), with \(M_v\) a large constant for any \(v\,\in \,V\). The cost function is convex decreasing and it is equivalent to \(b_v(x_v)\) being a concave increasing function. We use benefit function rather than cost function.
- 2.
This PTAS also works for multiple choice and constant dimensional knapsack problem, which will be used for PG with polynomial size integer variables.
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Anastasiadis, E., Deng, X., Krysta, P., Li, M., Qiao, H., Zhang, J. (2016). New Results for Network Pollution Games. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_4
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