Carpooling in social networks

Amos Fiat, Anna R. Karlin, Elias Koutsoupias, Claire Mathieu, Rotem Zach

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider the online carpool fairness problem of [Fagin and Williams, 1983] in which an online algorithm is presented with a sequence of pairs drawn from a group of n potential drivers. The online algorithm must select one driver from each pair, with the objective of partitioning the driving burden as fairly as possible for all drivers. The unfairness of an online algorithm is a measure of the worst-case deviation between the number of times a person has driven and the number of times they would have driven if life was completely fair. We introduce a version of the problem in which drivers only carpool with their neighbors in a given social network graph; this is a generalization of the original problem, which corresponds to the social network of the complete graph. We show that for graphs of degree d, the unfairness of deterministic algorithms against adversarial sequences is exactly d/2. For random sequences of edges from planar graph social networks we give a [deterministic] algorithm with logarithmic unfairness (holds more generally for any bounded-genus graph). This does not follow from previous random sequence results in the original model, as we show that restricting the random sequences to sparse social network graphs may increase the unfairness. A very natural class of randomized online algorithms are so-called static algorithms that preserve the same state distribution over time. Surprisingly, we show that any such algorithm has unfairness θ(√d) against oblivious adversaries. This shows that the local random greedy algorithm of [Ajtai et al, 1996] is close to optimal amongst the class of static algorithms. A natural (non-static) algorithm is global random greedy (which acts greedily and breaks ties at random). We improve the lower bound on the competitive ratio from Ω(log1/3(d)) to Ω(log d). We also show that the competitive ratio of global random greedy against adaptive adversaries is Ω(d).

Original languageEnglish
Title of host publication43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016
EditorsYuval Rabani, Ioannis Chatzigiannakis, Davide Sangiorgi, Michael Mitzenmacher
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770132
StatePublished - 1 Aug 2016
Event43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016 - Rome, Italy
Duration: 12 Jul 201615 Jul 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016


  • Carpool problem
  • Competitive ratio
  • Fairness
  • Online algorithms
  • Randomized algorithms

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