DeepAI

# A Tight Bound for Stochastic Submodular Cover

We show that the Adaptive Greedy algorithm of Golovin and Krause (2011) achieves an approximation bound of (ln (Q/η)+1) for Stochastic Submodular Cover: here Q is the "goal value" and η is the smallest non-zero marginal increase in utility deliverable by an item. (For integer-valued utility functions, we show a bound of H(Q), where H(Q) is the Q^th Harmonic number.) Although this bound was claimed by Golovin and Krause in the original version of their paper, the proof was later shown to be incorrect by Nan and Saligrama (2017). The subsequent corrected proof of Golovin and Krause (2017) gives a quadratic bound of (ln(Q/η) + 1)^2. Other previous bounds for the problem are 56(ln(Q/η) + 1), implied by work of Im et al. (2016) on a related problem, and k(ln (Q/η)+1), due to Deshpande et al. (2016) and Hellerstein and Kletenik (2018), where k is the number of states. Our bound generalizes the well-known (ln m + 1) approximation bound on the greedy algorithm for the classical Set Cover problem, where m is the size of the ground set.

• 7 publications
• 4 publications
• 43 publications
03/20/2018

### An analysis of the Greedy Algorithm for Stochastic Set Cover

We show that the approximation ratio of the greedy algorithm for the sto...
04/05/2019

### Safe Disassociation of Set-Valued Datasets

Disassociation introduced by Terrovitis et al. is a bucketization based ...
08/12/2020

### Tight Bounds on Subexponential Time Approximation of Set Cover and Related Problems

We show that Set Cover on instances with N elements cannot be approximat...
10/31/2018

### Stochastic Submodular Cover with Limited Adaptivity

In the submodular cover problem, we are given a non-negative monotone su...
11/05/2018

### An estimation of the greedy algorithm's accuracy for a set cover problem instance

For the set cover problem, by modifying the approach that leads to the p...
05/10/2017

### Comments on the proof of adaptive submodular function minimization

We point out an issue with Theorem 5 appearing in "Group-based active qu...
07/04/2022

### Correlated Stochastic Knapsack with a Submodular Objective

We study the correlated stochastic knapsack problem of a submodular targ...