Dividing Splittable Goods Evenly and With Limited Fragmentation

Author Peter Damaschke

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Peter Damaschke

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Peter Damaschke. Dividing Splittable Goods Evenly and With Limited Fragmentation. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 9:1-9:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


A splittable good provided in n pieces shall be divided as evenly as possible among m agents, where every agent can take shares of at most F pieces. We call F the fragmentation. For F=1 we can solve the max-min and min-max problems in linear time. The case F=2 has neat formulations and structural characterizations in terms of weighted graphs. Here we focus on perfectly balanced solutions. While the problem is strongly NP-hard in general, it can be solved in linear time if m>=n-1, and a solution always exists in this case. Moreover, case F=2 is fixed-parameter tractable in the parameter 2m-n. The results also give rise to various open problems.
  • packing
  • load balancing
  • weighted graph
  • linear-time algorithm
  • parameterized algorithm


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