Abstract
The NP-complete Distinguishing Substring Selection problem (DSSS for short) asks, given a set of “good” strings and a set of “bad” strings, for a solution string which is, with respect to Hamming metric, “away” from the good strings and “close” to the bad strings.
Studying the parameterized complexity of DSSS, we show that DSSS is W[1]-hard with respect to its natural parameters. This, in particular, implies that a recently given polynomial-time approximation scheme (PTAS) by Deng et al. cannot be replaced by a so-called efficient polynomial-time approximation scheme (EPTAS) unless an unlikely collapse in parameterized complexity theory occurs.
By way of contrast, for a special case of DSSS, we present an exact fixed-parameter algorithm solving the problem efficiently. In this way, we exhibit a sharp border between fixed-parameter tractability and intractability results.
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References
Abrahamson, K.: Generalized string matching. SIAM Journal on Computing 16(6), 1039–1051 (1987)
Alber, J., Gramm, J., Niedermeier, R.: Faster exact solutions for hard problems: a parameterized point of view. Discrete Mathematics 229(1-3), 3–27 (2001)
Amir, A., Lewenstein, M., Porat, E.: Faster algorithms for string matching with k mismatches. In: Proc. of 11th ACM-SIAM SODA, pp. 794–803 (2000)
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation – Combinatorial Optimization Problems and their Approximability Properties. Springer, Heidelberg (1999)
Cesati, M., Trevisan, L.: On the efficiency of polynomial time approximation schemes. Information Processing Letters 64(4), 165–171 (1997)
Deng, X., Li, G., Li, Z., Ma, B., Wang, L.: A PTAS for Distinguishing (Sub)string Selection. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 740–751. Springer, Heidelberg (2002)
Downey, R.G.: Parameterized complexity for the skeptic (invited paper). In: Proc. of 18th IEEE Conference on Computational Complexity (July 2003)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)
Evans, P.A., Smith, A., Wareham, H.T.: The parameterized complexity of p-center approximate substring problems. Technical report TR01-149, Faculty of Computer Science, University of New Brunswick, Canada (2001)
Fellows, M.R.: Parameterized complexity: the main ideas and connections to practical computing. In: Fleischer, R., Moret, B.M.E., Schmidt, E.M. (eds.) Experimental Algorithmics. LNCS, vol. 2547, pp. 51–77. Springer, Heidelberg (2002)
Fellows, M.R., Gramm, J., Niedermeier, R.: On the parameterized intractability of Closest Substring and related problems. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 262–273. Springer, Heidelberg (2002)
Frances, M., Litman, A.: On covering problems of codes. Theory of Computing Systems 30, 113–119 (1997)
Gramm, J., Niedermeier, R., Rossmanith, P.: Exact solutions for Closest String and related problems. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 441–453. Springer, Heidelberg (2001)
Lanctot, J.K., Li, M., Ma, B., Wang, S., Zhang, L.: Distinguishing string selection problems. In: Proc. of 10th ACM-SIAM SODA, pp. 633–642 (1999)
Li, M., Ma, B., Wang, L.: On the Closest String and Substring Problems. Journal of the ACM 49(2), 157–171 (2002)
Li, M., Ma, B., Wang, L.: Finding similar regions in many sequences. Journal of Computer and System Sciences 65(1), 73–96 (2002)
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Gramm, J., Guo, J., Niedermeier, R. (2003). On Exact and Approximation Algorithms for Distinguishing Substring Selection. In: Lingas, A., Nilsson, B.J. (eds) Fundamentals of Computation Theory. FCT 2003. Lecture Notes in Computer Science, vol 2751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45077-1_19
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DOI: https://doi.org/10.1007/978-3-540-45077-1_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40543-6
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