Abstract
The paper contributes to the systematic study (started by Berman and Karpinski) of explicit approximability lower bounds for small occurrence optimization problems.We present parametrized reductions for some packing and covering problems, including 3-Dimensional Matching, and prove the best known inapproximability results even for highly restricted versions of them. For example, we show that it is NP-hard to approximate Max-3-DM within \( \frac{{139}} {{138}} \) even on instances with exactly two occurrences of each element. Previous known hardness results for bounded occurence case of the problem required that the bound is at least three, and even then no explicit lower bound was known.
New structural results which improve the known bounds for 3-regular amplifiers and hence the inapproximability results for numerous small occurrence problems studied earlier by Berman and Karpinski are also presented.
The author has been supported by EU-Project ARACNE, Approximation and Randomized Algorithms in Communication Networks, HPRN-CT-1999-00112.
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Chlebík, M., Chlebíková, J. (2003). Approximation Hardness for Small Occurrence Instances of NP-Hard Problems. In: Petreschi, R., Persiano, G., Silvestri, R. (eds) Algorithms and Complexity. CIAC 2003. Lecture Notes in Computer Science, vol 2653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44849-7_21
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DOI: https://doi.org/10.1007/3-540-44849-7_21
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