Die Another Day

  • Rudolf Fleischer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4475)


The Hydra was a many-headed monster from Greek mythology that would immediately replace a head that was cut off by one or two new heads. It was the second task of Hercules to kill this monster. In an abstract sense, a Hydra can be modeled as a tree where the leaves are the heads, and when a head is cut off some subtrees get duplicated. Different Hydra species differ by which subtress can be duplicated in which multiplicity. Using some deep mathematics, it had been shown that two classes of Hydra species must always die, independent of the order in which heads are cut off. In this paper we identify three properties for a Hydra that are necessary and sufficient to make it immortal or force it to die. We also give a simple combinatorial proof for this classification. Now, if Hercules had known this...


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Rudolf Fleischer
    • 1
  1. 1.Fudan University, Shanghai Key Laboratory of Intelligent Information Processing, Department of Computer Science and Engineering, Shanghai 200433China

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