1995
DOI: 10.1007/bf02570718
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Almost optimal set covers in finite VC-dimension

Abstract: We give a deterministic polynomial-time method for finding a set cover in a set system (X, ~') of dual VC-dimension d such that the size of our cover is at most a factor of O(d log(dc)) from the optimal size, c. For constant VCdimensional set systems, which are common in computational geometry, our method gives an O(logc) approximation factor. This improves the previous O(logl XI) bound of the greedy method and challenges recent complexity-theoretic lower bounds for set covers (which do not make any assumption… Show more

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Cited by 386 publications
(328 citation statements)
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“…The literature is too vast to list exhaustively here. See e.g., [18,19,20,21,22,23,24] and the references therein.…”
Section: Other Related Workmentioning
confidence: 99%
“…The literature is too vast to list exhaustively here. See e.g., [18,19,20,21,22,23,24] and the references therein.…”
Section: Other Related Workmentioning
confidence: 99%
“…The original problem is NP-hard [12], and so are many of its geometric analogues. Therefore, approximation algorithms have been largely investigated, and in general, one looks for a subset of F that completely covers U and whose size is near-optimal; approximation factors better than log |U | are provably difficult to achieve in the finite case [10,13], and constant factor approximations were obtained for only a few geometric versions [6] (see also [5]). In this paper, we relax the problem in a different direction: given a covering F of a set U , we look for a small subset of F that covers most of U .…”
Section: Introductionmentioning
confidence: 99%
“…The development of randomized algorithms for HSP and related combinatorial problems defined on range spaces of finite VC-dimension, initiated by seminal papers [1] and [6] established a new field in modern computational geometry.…”
Section: Introductionmentioning
confidence: 99%