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Polymatroid Prophet Inequalities [article]

Paul Duetting, Robert Kleinberg
2013 arXiv   pre-print
In this note we go one step further and show that the bound carries over to settings where the fractions that can be chosen are subject to a polymatroid constraint.  ...  Consider a gambler and a prophet who observe a sequence of independent, non-negative numbers. The gambler sees the numbers one-by-one whereas the prophet sees the entire sequence at once.  ...  Algorithm for Polymatroids Our algorithm for the polymatroid prophet inequality is based on the algorithm of Kleinberg and Weinberg [16] for the matroid prophet inequality.  ... 
arXiv:1307.5299v1 fatcat:ilmx6de6afduleu3mpmjkrbgsi

Polymatroid Prophet Inequalities [chapter]

Paul Dütting, Robert Kleinberg
2015 Lecture Notes in Computer Science  
In this note we go one step further and show that the bound carries over to settings where the fractions that can be chosen are subject to a polymatroid constraint.  ...  Consider a gambler and a prophet who observe a sequence of independent, non-negative numbers. The gambler sees the numbers one-by-one whereas the prophet sees the entire sequence at once.  ...  Algorithm for Polymatroids Our algorithm for the polymatroid prophet inequality is based on the algorithm of Kleinberg and Weinberg [16] for the matroid prophet inequality.  ... 
doi:10.1007/978-3-662-48350-3_37 fatcat:j7bmndkkfbfkph24mogxxda6k4

Beating 1-1/e for ordered prophets

Melika Abolhassani, Soheil Ehsani, Hossein Esfandiari, MohammadTaghi HajiAghayi, Robert Kleinberg, Brendan Lucier
2017 Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017  
In this paper we present a threshold-based algorithm for the prophet inequality with n iid distributions.  ...  Hill and Kertz studied the prophet inequality on iid distributions [The Annals of Probability 1982]. They proved a theoretical bound of 1-1/e on the approximation factor of their algorithm.  ...  Prophet inequalities have been studied under complicated combinatorial structures such as matroid, polymatroid, and matching.  ... 
doi:10.1145/3055399.3055479 dblp:conf/stoc/AbolhassaniEEHK17 fatcat:duznom5ivvad3mly2go6pdcrsi

Mechanism with unique learnable equilibria

Paul Dütting, Thomas Kesselheim, Éva Tardos
2014 Proceedings of the fifteenth ACM conference on Economics and computation - EC '14  
We also show that our uniqueness result extends to problems with polymatroid structure under some conditions.  ...  Prophet inequalities for matroids and polymatroids are given in [Kleinberg and Weinberg 2012] and [Dütting and Kleinberg 2013] .  ...  In a sequence of papers, Hajiaghayi et al. [2007] , Chawla et al. [2010] , and Alaei [2011] show how algorithms for proving so-called prophet inequalities can be turned into truthful approximation  ... 
doi:10.1145/2600057.2602838 dblp:conf/sigecom/DuttingKT14 fatcat:5vv7xnfqxbcbjl6cbxirnlxbra

Improved Prophet Inequalities for Combinatorial Welfare Maximization with (Approximately) Subadditive Agents

Hanrui Zhang, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
We give a framework for designing prophet inequalities for combinatorial welfare maximization.  ...  as a byproduct, an O(1)-competitive prophet inequality for submodular or fractionally subadditive (a.k.a.  ...  E S A 2 0 2 0 82:10 Improved Prophet Inequalities for Subadditive Agents Proof.  ... 
doi:10.4230/lipics.esa.2020.82 dblp:conf/esa/Zhang20 fatcat:4urerxq725d2voqx2a22f6gd6e

Online Stochastic Max-Weight Matching: prophet inequality for vertex and edge arrival models [article]

Tomer Ezra, Michal Feldman, Nick Gravin, Zhihao Gavin Tang
2020 arXiv   pre-print
Interestingly, a pricing-based prophet inequality with comparable competitive ratios is unknown.  ...  We provide prophet inequality algorithms for online weighted matching in general (non-bipartite) graphs, under two well-studied arrival models, namely edge arrival and vertex arrival.  ...  In Section 2.2 we extend the notion of prophet inequality to batched prophet inequality. In Section 2.3 we establish a reduction from batched prophet inequality to batched OCRS.  ... 
arXiv:2002.09807v2 fatcat:nvoue6y6nbag3nyg3bsk6j27xm

Beyond matroids: Secretary Problem and Prophet Inequality with general constraints [article]

Aviad Rubinstein
2016 arXiv   pre-print
We study generalizations of the "Prophet Inequality" and "Secretary Problem", where the algorithm is restricted to an arbitrary downward-closed set system.  ...  In Prophet Inequality, the order is adversarial, but the values are drawn from known, independent but not identical distributions.  ...  Introduction The "Secretary Problem" and "Prophet Inequality" and their variants have been central problems in optimal stopping theory for decades.  ... 
arXiv:1604.00357v1 fatcat:o7vjny3zenglrnhnpeqswu77bu

Prophet inequality for bipartite matching: merits of being simple and non adaptive [article]

Nick Gravin, Hongao Wang
2019 arXiv   pre-print
Kleinberg and Wienberg STOC 12] for the intersection of two matroids in two ways: our policy is non adaptive and has better approximation guarantee of 3 instead of previous guarantee of 5.82 against the prophet  ...  Prophet inequalities were obtained for a variety of multiple choice combinatorial settings: for matroid and intersection of matroids [KW12, AKW14, FSZ16] , polymatroids [DK15] , the generalized assignment  ...  Similar to the previous literature on the prophet inequality in the strategic settings (e.g.  ... 
arXiv:1902.06243v1 fatcat:llhwytiw6rfq5gqpgnlhkiqzgm

Prophet Secretary for Combinatorial Auctions and Matroids [chapter]

Soheil Ehsani, MohammadTaghi Hajiaghayi, Thomas Kesselheim, Sahil Singla
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
The secretary and the prophet inequality problems are central to the field of Stopping Theory.  ...  [FGL15] show that for adversarial arrival order of random variables the optimal prophet inequalities give a 1/2-approximation.  ...  For the intersection of p matroids, Kleinberg and Weinberg [KW12] give an O(p)-approximation prophet inequality. Dütting and Kleinberg [DK15] extend this result to polymatroids. Feldman et al.  ... 
doi:10.1137/1.9781611975031.46 dblp:conf/soda/EhsaniHKS18 fatcat:tgumcl4ftbhbpk575oywg5mtue

Prophet Secretary for Combinatorial Auctions and Matroids [article]

Soheil Ehsani, MohammadTaghi Hajiaghayi, Thomas Kesselheim, Sahil Singla
2018 arXiv   pre-print
The secretary and the prophet inequality problems are central to the field of Stopping Theory.  ...  For such a random arrival model, we improve upon the 1/2-approximation and obtain (1-1/e)-approximation prophet inequalities for both matroids and combinatorial auctions.  ...  For the intersection of p matroids, Kleinberg and Weinberg [KW12] give an O(p)-approximation prophet inequality. Dütting and Kleinberg [DK15] extend this result to polymatroids. Feldman et al.  ... 
arXiv:1710.11213v2 fatcat:uatlejldrvcjjamcy6n72ee4k4

Static pricing for multi-unit prophet inequalities [article]

Shuchi Chawla, Nikhil Devanur, Thodoris Lykouris
2021 arXiv   pre-print
Prior to our work, the best competitive ratio known for this setting was the 1/2 that follows from the single-unit prophet inequality.  ...  When k=1, this is the so called "prophet inequality" problem for which there is a simple pricing scheme achieving a competitive ratio of 1/2.  ...  Polymatroid prophet inequalities.  ... 
arXiv:2007.07990v2 fatcat:ka37h7wrjjhktjshkfdse5regy

Prophet Inequalities via the Expected Competitive Ratio [article]

Tomer Ezra and Stefano Leonardi and Rebecca Reiffenhäuser and Matteo Russo and Alexandros Tsigonias-Dimitriadis
2022 arXiv   pre-print
We consider prophet inequalities under general downward-closed constraints.  ...  In a prophet inequality problem, a decision-maker sees a series of online elements and needs to decide immediately and irrevocably whether or not to select each element upon its arrival, subject to an  ...  Introduction Prophet Inequalities are one of optimal stopping theory's most prominent problem classes.  ... 
arXiv:2207.03361v2 fatcat:qvabhh72u5duvlm355gnhhcl5u

An Improved Lower Bound for Matroid Intersection Prophet Inequalities [article]

Raghuvansh R. Saxena, Santhoshini Velusamy, S. Matthew Weinberg
2022 arXiv   pre-print
We consider prophet inequalities subject to feasibility constraints that are the intersection of q matroids.  ...  Definition 2.5 (Approximability of a Prophet Inequality Instance).  ...  Matroid Intersection Prophet Inequalities We briefly formally define terminology that we will use when discussing approximation guarantees of prophet inequalities.  ... 
arXiv:2209.05614v1 fatcat:xe673jpmpzb47k67u6chowhueu

Prophets and Secretaries with Overbooking [article]

Tomer Ezra and Michal Feldman and Ilan Nehama
2019 arXiv   pre-print
The prophet and secretary problems demonstrate online scenarios involving the optimal stopping theory.  ...  We give upper and lower bounds on the competitive ratio of ℓ-out-of-k prophet and secretary scenarios.  ...  A single-sample algorithm ALG is said to induce an ℓ-out-of-k prophet inequality with a competitive ratio ρ if top ℓ (ALG(D 2 )) ≥ ρ · top ℓ (D).  ... 
arXiv:1805.05094v2 fatcat:wyebbsviw5h4jcaqf4c5mjtcca

Prophet Inequalities Made Easy: Stochastic Optimization by Pricing Non-Stochastic Inputs [article]

Paul Dütting, Michal Feldman, Thomas Kesselheim, Brendan Lucier
2017 arXiv   pre-print
The framework establishes prophet inequalities by constructing price-based online approximation algorithms, a natural extension of threshold algorithms for settings beyond binary selection.  ...  Our framework unifies and simplifies much of the existing literature on prophet inequalities and posted price mechanisms, and is used to derive new and improved results for combinatorial markets (with  ...  Subsequently, threshold-based prophet inequalities and postedprice mechanisms were developed for matroids and matroid intersection [13, 33, 7] , polymatroids [20] , unit-demand bidders [13, 3] , and  ... 
arXiv:1612.03161v2 fatcat:exaa5jinkbdshbq2bl7dvzb3vq
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