Inapproximability of Maximal Strip Recovery

  • Authors:

  • Minghui Jiang

  • Affiliations:

  • Department of Computer Science, Utah State University, Logan, USA 84322-4205

  • Venue:
  • ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
  • Year:
  • 2009

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Abstract

In comparative genomic, the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes. For the reliable recovery of syntenic blocks, noise and ambiguities in the genomic maps need to be removed first. Maximal Strip Recovery (MSR) is an optimization problem recently proposed by Zheng, Zhu, and Sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities. Given d genomic maps as sequences of gene markers, the objective of MSR-d is to find d subsequences, one subsequence of each genomic map, such that the total length of the syntenic blocks (substrings of consecutive gene markers that appear identically in all d subsequences) is maximized. A polynomial-time 2d-approximation for MSR-d was previously known. In this paper, we show that even the most basic version of MSR-2, in which all gene markers are distinct and in positive orientation, is APX-hard. Moreover, we provide the first explicit lower bounds on approximating MSR-d for all constants d 驴 2.