Improved Bounds in Stochastic Matching and Optimization

We consider two fundamental problems in stochastic optimization: approximation algorithms for stochastic matching, and sampling bounds in the black-box model. For the former, we improve the current-best bound of 3.709 due to Adamczyk et al. (2015), to 3.224; we also present improvements on Bansal et al. (2012) for hypergraph matching and for relaxed versions of the problem. In the context of stochastic optimization, we improve upon the sampling bounds of Charikar et al. (2005).

[1]  Alexander Shapiro,et al.  Lectures on Stochastic Programming: Modeling and Theory , 2009 .

[2]  Atri Rudra,et al.  When LP is the Cure for Your Matching Woes: Approximating Stochastic Matchings , 2010, ArXiv.

[3]  Atri Rudra,et al.  When LP Is the Cure for Your Matching Woes: Improved Bounds for Stochastic Matchings , 2010, Algorithmica.

[4]  David P. Williamson,et al.  The Design of Approximation Algorithms , 2011 .

[5]  Nicole Immorlica,et al.  On the costs and benefits of procrastination: approximation algorithms for stochastic combinatorial optimization problems , 2004, SODA '04.

[6]  Chaitanya Swamy,et al.  An approximation scheme for stochastic linear programming and its application to stochastic integer programs , 2006, JACM.

[7]  Amit Kumar,et al.  A constant-factor approximation for stochastic Steiner forest , 2009, STOC '09.

[8]  Piotr Sankowski,et al.  Stochastic analyses for online combinatorial optimization problems , 2008, SODA '08.

[9]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[10]  Atri Rudra,et al.  Approximating Matches Made in Heaven , 2009, ICALP.

[11]  Aravind Srinivasan,et al.  Selling Tomorrow's Bargains Today , 2015, AAMAS.

[12]  E. Chong,et al.  Wiley‐Interscience Series in Discrete Mathematics and Optimization , 2011 .

[13]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[14]  E. Beale ON MINIMIZING A CONVEX FUNCTION SUBJECT TO LINEAR INEQUALITIES , 1955 .

[15]  Jan Vondrák,et al.  Approximating the stochastic knapsack problem: the benefit of adaptivity , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[16]  David B. Shmoys,et al.  Approximation Algorithms for Stochastic Inventory Control Models , 2005, Math. Oper. Res..

[17]  Fabrizio Grandoni,et al.  Improved Approximation Algorithms for Stochastic Matching , 2015, ESA.

[18]  George B. Dantzig,et al.  Linear Programming Under Uncertainty , 2004, Manag. Sci..

[19]  Rajiv Gandhi,et al.  Dependent rounding and its applications to approximation algorithms , 2006, JACM.

[20]  R. Ravi,et al.  An edge in time saves nine: LP rounding approximation algorithms for stochastic network design , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[21]  Zoltán Füredi,et al.  On the fractional matching polytope of a hypergraph , 1993, Comb..

[22]  Aravind Srinivasan,et al.  Approximation algorithms for stochastic and risk-averse optimization , 2007, SODA '07.

[23]  Aravind Srinivasan,et al.  Finding Large Independent Sets in Graphs and Hypergraphs , 2005, SIAM J. Discret. Math..

[24]  R. Ravi,et al.  Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems , 2004, Math. Program..