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Parameterized lower bound and inapproximability of polylogarithmic string barcoding

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Abstract

String barcoding is a method that can identify microorganisms by analyzing their genome sequences. In this paper, we study the polylogarithmic string barcoding problem, where the lengths of the substrings in the testing set are polylogarithmically bounded. In particular, we show that the polylogarithmic string barcoding problem remains NP-hard and moreover, for a problem instance with n sequences, it is NP-hard to achieve an approximate ratio within dln n in polynomial time, where d is some constant. We then consider the parameterized polylogarithmic string barcoding problem, where the number of substrings in the test set is considered to be a fixed parameter k. We show that, unless W[2]=FPT, there does not exist a 2O(k) n c algorithm that can decide whether a test set of size k exists or not, where c is a constant independent of n and k.

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Authors and Affiliations

  1. Department of Systems and Computer Science, Howard University, Washington, DC, 20059, USA

    Chunmei Liu & Legand L. Burge

  2. Department of Mathematics and Computer Science, University of Maryland Eastern Shore, Princess Anne, MD, 21853, USA

    Yinglei Song

Authors
  1. Chunmei Liu
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  2. Yinglei Song
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  3. Legand L. Burge
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Correspondence to Chunmei Liu.

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Liu, C., Song, Y. & Burge, L.L. Parameterized lower bound and inapproximability of polylogarithmic string barcoding. J Comb Optim 16, 39–49 (2008). https://doi.org/10.1007/s10878-007-9097-x

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  • DOI: https://doi.org/10.1007/s10878-007-9097-x

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