Network Pollution Games

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

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Author(s)

  • Eleftherios Anastasiadis
  • Xiaotie Deng
  • Piotr Krysta
  • Han Qiao
  • Jinshan Zhang

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)124-166
Journal / PublicationAlgorithmica
Volume81
Issue number1
Early online date2 Apr 2018
Publication statusPublished - Jan 2019

Link(s)

Abstract

The problem of pollution control has been mainly studied in the environmental economics literature where the methodology of game theory is applied for the pollution control. To the best of our knowledge this is the first time this problem is studied from the computational point of view. We introduce a new network model for pollution control and present two applications of this model. On a high level, our model comprises a graph whose nodes represent the agents, which can be thought of as the sources of pollution in the network. The edges between agents represent the effect of spread of pollution. The government who is the regulator, is responsible for the maximization of the social welfare and sets bounds on the levels of emitted pollution in both local areas as well as globally in the whole network. We first prove that the above optimization problem is NP-hard even on some special cases of graphs such as trees. We then turn our attention on the classes of trees and planar graphs which model realistic scenarios of the emitted pollution in water and air, respectively. We derive approximation algorithms for these two kinds of networks and provide deterministic truthful and truthful in expectation mechanisms. In some settings of the problem that we study, we achieve the best possible approximation results under standard complexity theoretic assumptions. Our approximation algorithm on planar graphs is obtained by a novel decomposition technique to deal with constraints on vertices. We note that no known planar decomposition techniques can be used here and our technique can be of independent interest. For trees we design a two level dynamic programming approach to obtain an FPTAS. This approach is crucial to deal with the global pollution quota constraint. It uses a special multiple choice, multi-dimensional knapsack problem where coefficients of all constraints except one are bounded by a polynomial of the input size. We furthermore derive truthful in expectation mechanisms on general networks with bounded degree.

Research Area(s)

  • Algorithmic mechanism design, Approximation algorithms, Planar graphs, Pollution control

Citation Format(s)

Network Pollution Games. / Anastasiadis, Eleftherios; Deng, Xiaotie; Krysta, Piotr; Li, Minming; Qiao, Han; Zhang, Jinshan.

In: Algorithmica, Vol. 81, No. 1, 01.2019, p. 124-166.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

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