This paper studies approximation algorithm for the maximum weight budgeted connected set cover (MWBCSC) problem. Given an element set , a collection of sets , a weight function on , a cost function on , a connected graph (called communication graph) on vertex set , and a budget , the MWBCSC problem is to select a subcollection such that the cost , the subgraph of induced by is connected, and the total weight of elements covered by (that is ) is maximized. We present a polynomial time algorithm for this problem with a natural communication graph that has performance ratio , where is the maximum degree of graph and is the number of sets in . In particular, if every set has cost at most , the performance ratio can be improved to .
- Budgeted set cover; Connected set cover; Approximation algorithm