an:06292389
Zbl 1288.05177
Arulselvan, Ashwin
A note on the set union knapsack problem
EN
Discrete Appl. Math. 169, 214-218 (2014).
0166-218X
2014
j
05C60 05C42 90C10 68W25
approximation; densest \(k\)-subgraph; set-union knapsack; greedy
Summary: Recently, \textit{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.
1002.68203