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Abstract: This paper examines the complexity of several geometric problems due to unbounded dimension. The problems considered are: (i) minimum cover of points by unit cubes, (ii) minimum cover of points by unit balls, and (iii) minimum number of lines to hit a set of balls. Each of these problems is proven not to have a polynomial approximation scheme unless P = NP. Specific lower bounds on the error ratios attainable in polynomial time are given, assuming P<F NaN> 6= NP. In particular, it is shown that ... (Update)
Context of citations to this paper: More
.... most facility location problems are NP hard, even in the plane or even when only an approximate solution is being sought [101, 113, 159, 186, 187, 167]. Although many of these problems can be solved in polynomial time for a fixed value of p, some of them still remain...
.... most facility location problems are NP Hard, even in the plane or even when only an approximate solution is being sought [76, 88, 120, 130, 143, 144]. Although many of these problems can be solved in polynomial time for a xed value of p, some of them still remain intractable....
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BibTeX entry: (Update)
N. Megiddo, On the complexity of some geometric problems in unbounded dimension, J. Symbolic Comput., 10 (1990), 327--334. http://citeseer.ist.psu.edu/megiddo90complexity.html More
@article{ megiddo90complexity,
author = "Nimrod Megiddo",
title = "On the Complexity of Some Geometric Problems in Unbounded Dimension",
journal = "Journal of Symbolic Computation",
volume = "10",
number = "3/4",
pages = "327-334",
year = "1990",
url = "citeseer.ist.psu.edu/megiddo90complexity.html" }
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129 A Polynomial algorithm in linear programming (context) - Khachiyan - 1979
74 Approximation schemes for covering and packing problems in i.. (context) - Hochbaum, Maass - 1985
69 Optimal packing and covering in the plane are NP-complete (context) - Fowler, Paterson et al. - 1981
57 the complexity of some common geometric location problems (context) - Megiddo, Supowit - 1984
26 the complexity of polyhedral separability - Megiddo - 1988
10 Approximation algorithms for hitting objects by straight lin.. (context) - Hassin, Megiddo - 1990
3 The weighted Euclidean 1-center problem (context) - Chandrasekaran - 1982
The graph only includes citing articles where the year of publication is known.
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