Sequencing from Compomers: The Puzzle

The board game FragmindTM poses the following problem: The player has to reconstruct an (unknown) string s over the alphabet . To this end, the game reports the following information to the player, for every character x : First, the string s is cleaved wherever the character x is found in s. Second, every resulting fragment y is scrambled by a random permutation so that the only information left is how many times y contains each character . These scrambled fragments are then reported to the player. Clearly, distinct strings can show identical cleavage patterns for all cleavage characters. In fact, even short strings of length 30+ usually have non-unique cleavage patterns. To this end, we introduce a generalization of the game setup called Sequencing from Compomers. We also generate those fragments of s that contain up to k uncleaved characters x, for some small and fixed threshold k. This modification dramatically increases the length of strings that can be uniquely reconstructed. W...

• Type: Journal
• Year: 2006
• Where: MST
• Authors: Sebastian Böcker
• Keywords: Board Game Fragmindtm, Cleavage Patterns, Identical Cleavage Patterns, MST 2006