1 is simply called the Set Cover problem and denoted by SC; we will denote an instance of SC simply by <n,m>instead of <n,m,1>. Both SC and SC k are already well-known in the realm of design and analysis of combinatorial algorithms (e.g., see [18]). Let 3 ≤ a<ndenote the maximum number of elements in any set, i.e., a = max i∈[1,m]{|S i ...

Home remedies for rahu ketu doshaGreedy algorithm can give us an approximation ratio of lnn, that is, k ≤ k ∗ lnn. The greedy algorithm is very intuitive: in each iteration, select the set that has the maximum uncovered elements; keep iterating until we cover all elements.

Let f: 2 N → R + be a non-decreasing submodular set function, and let (N, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2-approximation [9] for this problem.