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Stochastic Covering and Adaptivity [chapter]

Michel Goemans, Jan Vondrák
2006 Lecture Notes in Computer Science  
This is a natural counterpart to the stochastic packing problems introduced in [5] .  ...  In the model without item multiplicity, we show that the adaptivity gap for Stochastic Set Cover can be Ω(d).  ...  Thus we have a d-approximation, but this approximation algorithm is adaptive so it doesn't settle the adaptivity gap for Stochastic Set Packing. The final answer is unknown.  ... 
doi:10.1007/11682462_50 fatcat:gkymtysxzfdaniy53yl7hetcva

A Stochastic Probing Problem with Applications [chapter]

Anupam Gupta, Viswanath Nagarajan
2013 Lecture Notes in Computer Science  
We study a general stochastic probing problem defined on a universe V , where each element e ∈ V is "active" independently with probability pe.  ...  Our results provide a simple and unified view of results in stochastic matching [1, 2] and Bayesian mechanism design [3], and can also handle more general constraints.  ...  We also thank an anonymous reviewer for pointing out that the LP for weighted stochastic probing can be solved approximately for general k-systems.  ... 
doi:10.1007/978-3-642-36694-9_18 fatcat:ynz3ypxcznhljlp4qahxpxklqm

Ignorance is Almost Bliss

Avrim Blum, John P. Dickerson, Nika Haghtalab, Ariel D. Procaccia, Tuomas Sandholm, Ankit Sharma
2015 Proceedings of the Sixteenth ACM Conference on Economics and Computation - EC '15  
This guarantee is close to the best known polynomial-time approximation ratio of 3/k+1 -ϵ for the deterministic k-set packing problem [Furer and Yu, 2013] We empirically explore the application of (adaptations  ...  Our main theoretical result for the stochastic matching (i.e., 2-set packing) problem is the design of an adaptive algorithm that queries only a constant number of edges per vertex and achieves a (1-ϵ)  ...  Algorithm 4 ADAPTIVE ALGORITHM FOR STOCHASTIC k-SET PACKING Input: A k-set instance (U, A), and > 0.  ... 
doi:10.1145/2764468.2764479 dblp:conf/sigecom/BlumDHPSS15 fatcat:loefmact5rgbveyafmesg6zf64

The Price of Information in Combinatorial Optimization [chapter]

Sahil Singla
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
We give a technique that reduces such problems to their non-price counterparts, and use it to design exact/approximation algorithms to optimize our utility/disutility.  ...  We are grateful to Anupam Gupta and Viswanath Nagarajan for several discussions on this project.  ...  Acknowledgments We thank Anupam Gupta, Guru Prashanth, Bobby Kleinberg, and Akanksha Bansal for helpful comments on improving the presentation of this paper.  ... 
doi:10.1137/1.9781611975031.161 dblp:conf/soda/Singla18 fatcat:ffxlb43y4bdmrico7jzsvcb2fm

Stochastic Combinatorial Optimization via Poisson Approximation [article]

Jian Li, Wen Yuan
2013 arXiv   pre-print
We study several stochastic combinatorial problems, including the expected utility maximization problem, the stochastic knapsack problem and the stochastic bin packing problem.  ...  For the stochastic bin packing problem (introduced in [Kleinberg, Rabani and Tardos, STOC97]), we show there is a polynomial time algorithm which uses at most the optimal number of bins, if we relax the  ...  Acknowledgements We would like to thank Yinyu Ye and Uri Zwick for stimulating discussions.  ... 
arXiv:1211.1149v2 fatcat:6ynd4wpinbhzxjxsc4s7xzfhsi

Stochastic Packing Integer Programs with Few Queries [article]

Takanori Maehara, Yutaro Yamaguchi
2019 arXiv   pre-print
We propose a general framework of adaptive and non-adaptive algorithms for this problem, and provide a unified methodology for analyzing the performance of those algorithms.  ...  We consider a stochastic variant of the packing-type integer linear programming problem, which contains random variables in the objective vector.  ...  Acknowledgments The authors thank anonymous reviewers for their careful reading and a number of valuable comments. This work was supported by JSPS KAKENHI Grant Numbers 16H06931 and 16K16011.  ... 
arXiv:1707.04020v3 fatcat:myc72wakm5cnxovi35pp7ajoru

Online Bin Packing with Known T [article]

Shang Liu, Xiaocheng Li
2021 arXiv   pre-print
For the latter one, our analysis provides an alternative (probably simpler) treatment and tightens the analysis of the asymptotic benchmark of the stochastic bin packing problem in Rhee and Talagrand (  ...  We develop and analyze an adaptive algorithm that solves an offline bin packing problem at geometric time intervals and uses the offline optimal solution to guide online packing decisions.  ...  For the first part, the stochastic bin packing packing can be viewed as the analysis of the offline benchmark in the online bin packing problem.  ... 
arXiv:2112.03200v1 fatcat:37nelr2365ftrkvscqaoyk5rby

A Stochastic Probing Problem with Applications [article]

Anupam Gupta, Viswanath Nagarajan
2013 arXiv   pre-print
We study a general stochastic probing problem defined on a universe V, where each element e in V is "active" independently with probability p_e.  ...  Our results provide a simple and unified view of results in stochastic matching and Bayesian mechanism design, and can also handle more general constraints.  ...  We also thank an anonymous reviewer for pointing out that the LP for weighted stochastic probing can be solved approximately for general k-systems, which leads to an approximation algorithm for weighted  ... 
arXiv:1302.5913v1 fatcat:7pb6ph4tbvfezi7g6emrvjswrm

Stochastic Packing Integer Programs with Few Queries [chapter]

Yutaro Yamaguchi, Takanori Maehara
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
We propose a general framework of adaptive and non-adaptive algorithms for this problem, and provide a unified methodology for analyzing the performance of those algorithms.  ...  We consider a stochastic variant of the packing-type integer linear programming problem, which contains random variables in the objective vector.  ...  Acknowledgment The authors thank anonymous reviewers for their valuable comments. This work was supported by JSPS KAKENHI Grant Numbers 16H06931 and 16K16011.  ... 
doi:10.1137/1.9781611975031.21 dblp:conf/soda/YamaguchiM18 fatcat:ltoocexiive3xfixxyiuu7n6x4

Packing Problems in Transportation and Supply Chain: New Problems and Trends

Guido Perboli, Luca Gobbato, Francesca Perfetti
2014 Procedia - Social and Behavioral Sciences  
cuts, rotation and incompatibility between items, only recently they have started to consider more general issues as multi-attributes problems, rich packing problems, and uncertainty in the attributes.  ...  Even if packing problems are, from their beginning, strictly linked to Transportation, the recent advances in this field (Smart City, Last Mile integration, City Logistics) and long-term planning of cross-country  ...  for the Logistics Optimization", by the Natural Sciences and Engineering Council of Canada (NSERC) and the Fonds de recherche du Québec-Nature et technologies (FRQ_NT).  ... 
doi:10.1016/j.sbspro.2014.01.101 fatcat:qlx25zi7mbdofefaa565y4s3ii

Approximation Algorithms for Stochastic Combinatorial Optimization Problems

Jian Li, Yu Liu
2016 Journal of the Operations Research Society of China  
for designing approximation algorithms for stochastic combinatorial optimization problems, including the linear programming relaxation approach, boosted sampling, content resolution schemes, Poisson approximation  ...  Our purpose is to provide the readers a quick glimpse to the models, problems and techniques in this area, and hopefully inspire new contributions.  ...  We apologize in advance for the omission of any important results. We would like to thank Xiaodong Hu for inviting us to write the survey.  ... 
doi:10.1007/s40305-015-0116-9 fatcat:wewxh47vgjgazg3thpbnonreaq

The stochastic generalized bin packing problem

Guido Perboli, Roberto Tadei, Mauro M. Baldi
2012 Discrete Applied Mathematics  
The Generalized Bin Packing Problem (GBPP) is a recently introduced packing problem where, given a set of bins characterized by volume and cost and a set of items characterized by volume and profit (which  ...  By using the asymptotic theory of extreme values a deterministic approximation for the S-GBPP is derived.  ...  The Generalized Bin Packing Problem and its stochastic counterpart are presented in Sections 3 and 4, respectively.  ... 
doi:10.1016/j.dam.2011.10.037 fatcat:apizvqtdwnejthzf7o56g4zfbq

Page 566 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews  
Especially, linear mixed-integer models are proposed for two-dimensional packing problems of convex and nonconvex polygons.  ...  Summary: “In this paper the modeling of packing problems (cut- ting and allocation problems) is investigated.  ... 

Stochastic Monotone Submodular Maximization with Queries [article]

Takanori Maehara, Yutaro Yamaguchi
2020 arXiv   pre-print
We study a stochastic variant of monotone submodular maximization problem as follows.  ...  s result on the unweighted matching problem and Behnezhad and Reyhani's result on the weighted matching problem in both objective function and feasible domain.  ...  Our result has the stronger stochastic guarantee (that is, Because the set of k-set packings forms a k-exchange system, our result gives a strategy for the stochastic weighted k-set packing problem that  ... 
arXiv:1907.04083v2 fatcat:62p5ngw4gnfpdnjmow7rtqz4tq

When LP Is the Cure for Your Matching Woes: Improved Bounds for Stochastic Matchings [chapter]

Nikhil Bansal, Anupam Gupta, Jian Li, Julián Mestre, Viswanath Nagarajan, Atri Rudra
2010 Lecture Notes in Computer Science  
This is similar to the approach for stochastic packing problems considered by Dean et al. [9, 8] .  ...  Theorem 3 There is a 3.46-approximation algorithm for the unweighted stochastic matching problem in general graphs.  ...  We would like to thank Aravind Srinivasan for helpful discussions.  ... 
doi:10.1007/978-3-642-15781-3_19 fatcat:uokxdnlqkzbsxl3mddinzajm2y
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