# The Price of Information in Combinatorial Optimization

@inproceedings{Singla2018ThePO, title={The Price of Information in Combinatorial Optimization}, author={Sahil Singla}, booktitle={SODA}, year={2018} }

Consider a network design application where we wish to lay down a minimum-cost spanning tree in a given graph; however, we only have stochastic information about the edge costs. To learn the precise cost of any edge, we have to conduct a study that incurs a price. Our goal is to find a spanning tree while minimizing the disutility, which is the sum of the tree cost and the total price that we spend on the studies. In a different application, each edge gives a stochastic reward value. Our goal…

## 43 Citations

### Combinatorial Optimization Under Uncertainty ( Probing and Stopping-Time Algorithms )

- Computer Science
- 2017

This thesis studies models where the input is revealed to us element-by-element and the authors have to make irrevocable decisions and considers combinatorial problems when either they have stochastic knowledge about the input but the revelation order is chosen by an adversary or when there are probing constraints.

### Beating Greedy for Stochastic Bipartite Matching

- Computer ScienceSODA
- 2019

A linear program (LP) is used to upper bound the optimum achieved by any strategy in the maximum bipartite matching problem in stochastic settings, namely the query-commit and price-of-information models.

### Markov Game with Switching Costs

- Mathematics, Computer ScienceArXiv
- 2021

This paper shows there is a simple index strategy that achieves a constant approximation factor if the switching cost is constant and k = 1, and proposes a more involved constant-factor approximation algorithm, via an nontrivial reduction to the stochastic k-TSP problem, in which a Markov chain is approximated by a random variable.

### The Markovian Price of Information

- MathematicsIPCO
- 2019

This paper proposes a strategy for advancing the Markov chains if the goal is to maximize the total reward minus the total price that the authors pay.

### Multi-token Markov Game with Switching Costs

- MathematicsSODA
- 2022

There is a simple index strategy that achieves a constant approximation factor if the switching cost is constant and k = 1 for a general Markovian MAB variant with switching costs, and this index strategy is the best of the knowledge.

### Online Allocation and Pricing: Constant Regret via Bellman Inequalities

- Computer ScienceOper. Res.
- 2021

This work develops a framework for designing simple and efficient policies for a family of online allocation and pricing problems that includes online packing, budget-constrained probing, dynamic pricing, and online contextual bandits with knapsacks, based on Bellman inequalities.

### Pandora's Box Problem with Order Constraints

- Computer ScienceEC
- 2020

It is proved that finding approximately optimal adaptive search strategies is NP-hard when certain matroid constraints are used to further restrict the set of boxes which may be opened, or when the order constraints are given as reachability constraints on a DAG.

### Random Order Vertex Arrival Contention Resolution Schemes for Matching, with Applications

- Computer Science, MathematicsICALP
- 2021

These results are the first non-trivial results for random order prophet matching and Price-of-Information matching in general graphs.

### Decentralized Matching in a Probabilistic Environment

- Computer ScienceEC
- 2021

This work considers a model for repeated stochastic matching where compatibility is probabilistic, is realized the first time agents are matched, and persists in the future, and demonstrates that the above process provides a 0.316-approximation to the optimal online algorithm for matching on general graphs.

### Stochastic Monotone Submodular Maximization with Queries

- Mathematics, Computer ScienceArXiv
- 2019

It is proved that the problem admits a good query strategy if the feasible domain has a uniform exchange property, and generalizes Blum et al.'s result on the unweighted matching problem and Behnezhad and Reyhani's results on the weighted matching problem in both objective function and feasible domain.

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