Unshuffling a square is NP-hard

  • Authors:

  • Sam Buss;Michael Soltys

  • Affiliations:

  • Dept. of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA;Dept. of Computing & Software, McMaster University, Hamilton, ON L8S 4K1, Canada

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2014

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Abstract

A shuffle of two strings is formed by interleaving the characters into a new string, keeping the characters of each string in order. A string is a square if it is a shuffle of two identical strings. There is a known polynomial time dynamic programming algorithm to determine if a given string z is the shuffle of two given strings x, y; however, it has been an open question whether there is a polynomial time algorithm to determine if a given string z is a square. We resolve this by proving that this problem is NP-complete via a many-one reduction from 3-Partition.