We study the problem of maximizing constrained non-monotone submodular
functions and provide approximation algorithms that improve existing algorithms
in terms of either the approximation factor or simplicity. Our algorithms
combine existing local search and greedy based algorithms. Different
constraints that we study are (exact) cardinality and knapsack constraints. For
the multiple-knapsack constraints we achieve a $(\frac{1}{4}-3\epsilon)$-factor
algorithm.