An Improved Envy-Free Cake Cutting Protocol for Four Agents

  • Georgios Amanatidis
  • George Christodoulou
  • John Fearnley
  • Evangelos Markakis
  • Christos-Alexandros Psomas
  • Eftychia Vakaliou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11059)


We consider the classic cake-cutting problem of producing envy-free allocations, restricted to the case of four agents. The problem asks for a partition of the cake to four agents, so that every agent finds her piece at least as valuable as every other agent’s piece. The problem has had an interesting history so far. Although the case of three agents is solvable with less than 15 queries, for four agents no bounded procedure was known until the recent breakthroughs of Aziz and Mackenzie [2, 3]. The main drawback of these new algorithms, however, is that they are quite complicated and with a very high query complexity. With four agents, the number of queries required is close to 600. In this work we provide an improved algorithm for four agents, which reduces the current complexity by a factor of 3.4. Our algorithm builds on the approach of [3] by incorporating new insights and simplifying several steps. Overall, this yields an easier to grasp procedure with lower complexity.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Georgios Amanatidis
    • 1
  • George Christodoulou
    • 2
  • John Fearnley
    • 2
  • Evangelos Markakis
    • 3
  • Christos-Alexandros Psomas
    • 4
  • Eftychia Vakaliou
    • 3
  1. 1.Centrum Wiskunde & Informatica (CWI)AmsterdamNetherlands
  2. 2.University of LiverpoolLiverpoolUK
  3. 3.Athens University of Economics and BusinessAthensGreece
  4. 4.Carnegie Mellon UniversityPittsburghUSA

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