DeepAI

# Random Order Set Cover is as Easy as Offline

We give a polynomial-time algorithm for OnlineSetCover with a competitive ratio of O(log mn) when the elements are revealed in random order, essentially matching the best possible offline bound of O(log n) and circumventing the Ω(log m log n) lower bound known in adversarial order. We also extend the result to solving pure covering IPs when constraints arrive in random order. The algorithm is a multiplicative-weights-based round-and-solve approach we call LearnOrCover. We maintain a coarse fractional solution that is neither feasible nor monotone increasing, but can nevertheless be rounded online to achieve the claimed guarantee (in the random order model). This gives a new offline algorithm for SetCover that performs a single pass through the elements, which may be of independent interest.

• 48 publications
• 6 publications
• 4 publications
10/18/2021

### Machine Covering in the Random-Order Model

In the Online Machine Covering problem jobs, defined by their sizes, arr...
10/22/2021

### The Log-Interleave Bound: Towards the Unification of Sorting and the BST Model

We study the connections between sorting and the binary search tree mode...
09/02/2020

### Fully-Dynamic Submodular Cover with Bounded Recourse

In submodular covering problems, we are given a monotone, nonnegative su...
09/09/2021

### Improved Online Algorithm for Fractional Knapsack in the Random Order Model

The fractional knapsack problem is one of the classical problems in comb...
01/20/2023

### Superpolynomial Lower Bounds for Learning Monotone Classes

Koch, Strassle, and Tan [SODA 2023], show that, under the randomized exp...
09/10/2019

### The Outer Limits of Contention Resolution on Matroids and Connections to the Secretary Problem

Contention resolution schemes have proven to be a useful and unifying ab...
10/17/2021

### Online Facility Location with Predictions

We provide nearly optimal algorithms for online facility location (OFL) ...