Titlebook: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques; 14th International W Leslie Ann Goldberg,Klaus Jan

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Opaque Setse barrier is restricted to the interior and the boundary of the input polygon, then the problem admits a fully polynomial-time approximation scheme for the connected case and a quadratic-time exact algorithm for the single-arc case. These are the first approximation algorithms obtained for this problem.

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On Capacitated Set Cover Problemsitated problem is closely related to that of the uncapacitated version. We also give related lower bounds, and show that the hereditary property is necessary to obtain non-trivial results. Finally, we give some results for capacitated covering problems on set systems with low hereditary discrepancy and low VC dimension.

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https://doi.org/10.1007/BFb0113620r the competitive ratio, and a strategy that achieves a ratio of 3; for different offline versions, we describe polynomial-time approximation schemes. For the MATP we show that no competitive ratio exists for the online problem, and give polynomial-time approximation schemes for offline versions.

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