On the Complexity of Positional Sequencing by Hybridization

In sequencing by hybridization (SBH), one has to reconstruct a sequence from its l-long substrings. SBH was proposed as an alternative to gel-based DNA sequencing approaches, but in its original form the method is not competitive. Positional SBH (PSBH) is a recently proposed enhancement of SBH in which one has additional information about the possible positions of each substring along the target sequence. We give a linear time algorithm for solving PSBH when each substring has at most two possible positions. On the other hand, we prove that the problem is NP-complete if each substring has at most three possible positions. We also show that PSBH is NP-complete if the set of allowed positions for each substring is an interval of length k, and provide a fast algorithm for the latter problem when k is bounded. Key Words: Positional Sequencing by Hybridization, Complexity, Eulerian Graphs, NP-Hardness, Parameterized Algorithms. 1 Introduction Sequencing by hybridization (SBH) was proposed ..