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Playing with the Maximum-Flow Problem

8 pagesPublished: October 23, 2018


In the traditional maximum-flow problem, the goal is to transfer maximum flow in a network by directing, in each vertex in the network, incoming flow into outgoing edges. The problem has been extensively used in order to optimize the performance of networks in numerous application areas. The definition of the problem corresponds to a setting in which the authority has control on all vertices of the network. Today’s computing environment involves parties that should be considered adversarial. We survey recent studies on flow games, which capture settings in which the vertices of the network are owned by different and selfish entities. We start with the case of two players, max (the authority), which aims at maximizing the flow, and min (the hostile environment), which aims at minimizing the flow. We argue that such flow games capture many modern settings, such as partially- controlled pipe or road systems or hybrid software-defined communication networks. We then continue to the special case where all vertices are owned by min. This case captures evacuation scenarios, where the goal is to maximize the flow that is guaranteed to travel in the most unfortunate routing decisions. Finally, we study the general case, of multiple players, each with her own target vertex. In all settings, we study the problems of finding the maximal flows, optimal strategies for the players, as well as stability and equilibrium inefficiency in the case of multi-player games. We discuss additional variants and their applications, and point to several interesting open problems.

In: Gilles Barthe, Geoff Sutcliffe and Margus Veanes (editors). LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 57, pages 18--25

BibTeX entry
  author    = {Orna Kupferman},
  title     = {Playing with the Maximum-Flow Problem},
  booktitle = {LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Gilles Barthe and Geoff Sutcliffe and Margus Veanes},
  series    = {EPiC Series in Computing},
  volume    = {57},
  pages     = {18--25},
  year      = {2018},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/tkk1}}
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