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A note on the set union knapsack problem. (English) Zbl 1288.05177
Summary: Recently, S. Khuller et al. [Inf. Process. Lett. 70, No.1, 39–45 (1999; Zbl 1002.68203)] presented a greedy algorithm for the budgeted maximum coverage problem. In this note, we observe that this algorithm also approximates a special case of a set-union knapsack problem within a constant factor. In the special case, an element is a member of less than a constant number of subsets. This guarantee naturally extends to densest $$k$$-subgraph problem on graphs of bounded degree.

##### MSC:
 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 05C42 Density (toughness, etc.) 90C10 Integer programming 68W25 Approximation algorithms
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##### References:
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