Abstract
We present in this paper differential approximation results for min set cover and min weighted set cover. We first show that the differential approximation ratio of the natural greedy algorithm for min set cover is bounded below by 1.365/\(\it \Delta\) and above by 4/(\(\it \Delta\) + 1), where \(\it \Delta\) is the maximum set-cardinality in the min set cover-instance. Next, we study an approximation algorithm for min weighted set cover and provide a tight lower bound of 1/\(\it \Delta\).
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Bazgan, C., Monnot, J., Paschos, V.T., Serrière, F. (2005). Greedy Differential Approximations for Min Set Cover. In: Vojtáš, P., Bieliková, M., Charron-Bost, B., Sýkora, O. (eds) SOFSEM 2005: Theory and Practice of Computer Science. SOFSEM 2005. Lecture Notes in Computer Science, vol 3381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30577-4_9
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DOI: https://doi.org/10.1007/978-3-540-30577-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24302-1
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