A Greedy Heuristic for the Set-Covering Problem

@article{Chvtal1979AGH,
  title={A Greedy Heuristic for the Set-Covering Problem},
  author={Vasek Chv{\'a}tal},
  journal={Math. Oper. Res.},
  year={1979},
  volume={4},
  pages={233-235}
}
  • V. Chvátal
  • Published 1 August 1979
  • Mathematics
  • Math. Oper. Res.
Let A be a binary matrix of size m × n, let cT be a positive row vector of length n and let e be the column vector, all of whose m components are ones. The set-covering problem is to minimize cTx subject to Ax ≥ e and x binary. We compare the value of the objective function at a feasible solution found by a simple greedy heuristic to the true optimum. It turns out that the ratio between the two grows at most logarithmically in the largest column sum of A. When all the components of cT are the… 
A greedy heuristic for a generalized set covering problem
TLDR
A greedy algorithm is proposed to approximate this generalized weighted set covering problem and an upper bound on the ratio of the greedy solution over the optimal solution is established, independent of the cost function, and it depends only on the total weight of the ground set.
A modified greedy algorithm for dispersively weighted 3-set cover
A Better-Than-Greedy Algorithm for k-Set Multicover
TLDR
This paper will verify that this is indeed the case by showing that such a modification of the classical greedy heuristic leads to an improved performance ratio of H(k)–1/6 for both versions of k-MC.
A note on the greedy approximation algorithm for the unweighted set covering problem
A simple greedy approximation algorithm for the unweighted set covering problem has been analyzed extensively in the literature. The common conclusion has been that in the worst case, the heuristic
1 RANDOMIZED HEURISTIC SHEMES FOR THE SET COVERING PROBLEM 1
TLDR
A general scheme to derive heuristics for the Set Covering Problem is proposed and embeds constructive Heuristics within a randomized procedure and introduces a random perturbation of the costs of the problem instance.
Using homogenous weights for approximating the partial cover problem
TLDR
It is shown that if the weights are homogeneous (i.e., proportional to the potential coverage of the sets) then any minimal cover is a good approximation, and it is sufficient to repeatedly subtract a homogeneous weight function from the given weight function.
Worst-Case Analysis of Greedy Heuristics for Integer Programming with Nonnegative Data
We give a worst-case analysis for two greedy heuristics for the integer programming problem minimize cx , Ax (ge) b , 0 (le) x (le) u , x integer, where the entries in A, b , and c are all
Set Covering Problems with General Objective Functions
TLDR
A parameterized version of set cover that generalizes several previously studied problems and derives an approximation ratio for a Rent-or-Buy set cover problem.
A note on the Clustered Set Covering Problem
...
1
2
3
4
5
...

References

SHOWING 1-4 OF 4 REFERENCES
Approximation Algorithms for Combinatorial Problems
On the ratio of optimal integral and fractional covers
The Design and Analysis of Computer Algorithms
TLDR
This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Integer Programming
The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization. This highly respected