  Due to much closer to real application scenarios,the budgeted influence
maximization (BIM) problem has attracted great attention among researchers. As
a variant of the influence maximization (IM) problem, the BIM problem aims at
mining several nodes with different costs as seeds with limited budget to
maximize the influence as possible. By first activating these seed nodes and
spreading influence under the given propagation model, the maximized spread of
influence can be reached in the network.
  Several approaches have been proposed for BIM. Most of them are modified
versions of the greedy algorithm, which work well on the IM but seems
inefficient for the BIM because huge time consuming is inevitable. Recently,
some intelligence algorithms are proposed in order to reduce the running time,
but analysis shows that they cannot fully utilize the relationships between
nodes in networks, which will result in influence loss.
  Inspired by this, we propose an efficient method based on boosted simulated
annealing (SA) algorithm in this paper. Three heuristic strategies are proposed
to improve the performance and speed up the proposed algorithm. Experimental
results on both real world and synthetic networks demonstrate that the proposed
boosted SA performs much better than existed algorithms on performance with
almost equal or less running time.
