Improved Guarantees for Offline Stochastic Matching via New Ordered Contention Resolution Schemes

Aravind Srinivasan; Brian Brubach; Calum MacRury; Nathaniel Grammel; Will Ma

arxiv: 2106.06892 · v3 · submitted 2021-06-13 · 💻 cs.DS · cs.DM

Improved Guarantees for Offline Stochastic Matching via New Ordered Contention Resolution Schemes

Brian Brubach , Nathaniel Grammel , Will Ma , Calum MacRury , Aravind Srinivasan This is my paper

Pith reviewed 2026-05-24 13:51 UTC · model grok-4.3

classification 💻 cs.DS cs.DM

keywords stochastic matchingcontention resolutionapproximation algorithmspatience constraintsprophet secretaryoffline algorithmsgeneral graphsbipartite graphs

0 comments

The pith

New ordered contention resolution schemes give a 0.382-approximation for stochastic matching in general graphs when every vertex has patience at least 2.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces new ordered contention resolution schemes to improve approximation ratios for stochastic matching problems where edge existence is uncertain and each vertex can probe only a limited number of neighbors. These schemes produce a 0.382-approximation algorithm for general graphs under the assumption that every vertex has patience at least 2, raising the prior guarantee of 0.31. The same techniques also deliver a 0.432-approximation via random-order probing when no patience limits apply, plus a 0.632-approximation for a restricted bipartite case with unit patience on one side. The results apply to offline settings where probabilities are known in advance and matches must be made irrevocably after probing.

Core claim

The central claim is that new ordered contention resolution schemes yield improved approximation guarantees for offline stochastic matching. For general graphs in which each vertex has patience at least 2, the schemes produce a 0.382-approximate algorithm, improving the previous 0.31 bound. When patience constraints are absent, random-order probing achieves a 0.432 approximation with corollaries that include a better guarantee for the prophet secretary problem under edge arrivals. For bipartite graphs with unit patience on one partition the same framework gives a 0.632 approximation.

What carries the argument

Ordered contention resolution schemes that fix a probing order among candidate edges to resolve contention while respecting independent edge probabilities and per-vertex patience limits.

If this is right

A 0.382-approximate algorithm exists for stochastic matching with patience at least 2 in general graphs.
A 0.432-approximate random-order probing algorithm exists for stochastic matching without patience constraints.
An improved approximation guarantee holds for the prophet secretary problem under edge arrivals.
A 0.632-approximate algorithm exists for bipartite stochastic matching with unit patience on one side.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The ordering idea may extend to other stochastic optimization settings where decisions must be made under uncertainty and irrevocable commitments.
If the independence assumption on edge probabilities is relaxed, the ratios would require separate analysis.
Implementation on concrete graph families could reveal whether the constants 0.382 and 0.432 are tight.

Load-bearing premise

Edge existences are independent, and the algorithm may irrevocably match an edge as soon as a probe succeeds while never exceeding any vertex's patience limit.

What would settle it

An explicit family of graphs with patience at least 2 for which the expected size of the matching produced by the algorithm is strictly less than 0.382 times the expected size of the optimal matching would falsify the 0.382 guarantee.

read the original abstract

Matching is one of the most fundamental and broadly applicable problems across many domains. In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching models. Here, each edge in the graph has a known, independent probability of existing derived from some prediction. Algorithms must probe edges to determine existence and match them irrevocably if they exist. Further, each vertex may have a patience constraint denoting how many of its neighboring edges can be probed. We present new ordered contention resolution schemes yielding improved approximation guarantees for some of the foundational problems studied in this area. For stochastic matching with patience constraints in general graphs, we provide a 0.382-approximate algorithm assuming each vertex has patience at least $2$. Under this assumption, we improve upon the previous best 0.31-approximation of Baveja et al. (2018). When the vertices do not have patience constraints, we describe a 0.432-approximate random order probing algorithm with several corollaries such as an improved guarantee for the Prophet Secretary problem under Edge Arrivals. Finally, for the special case of bipartite graphs with unit patience constraints on one of the partitions, we show a 0.632-approximate algorithm that improves on the recent $1/3$-guarantee of Hikima et al. (2021).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper improves approximation ratios for stochastic matching to 0.382 (patience >=2), 0.432 (no patience), and 0.632 (bipartite unit patience) via new ordered CRS, with no visible gaps in the claims.

read the letter

The main thing here is that the authors give concrete ratio improvements for offline stochastic matching by designing new ordered contention resolution schemes. For general graphs where every vertex has patience at least 2 they reach 0.382, up from the prior 0.31. Without patience constraints they get a 0.432 random-order probing algorithm that also yields a corollary for Prophet Secretary under edge arrivals. In the bipartite case with unit patience on one side they hit 0.632 against the recent 1/3 bound. These numbers are presented as strict gains over the cited earlier results, and the modeling assumptions (independent realizations, irrevocable matches on probe, per-vertex patience) are the usual ones for the problem and are stated plainly. The constructions appear to extend existing CRS ideas by imposing an order, which is a natural direction and seems to pay off in the stated regimes. The citation pattern tracks the relevant prior work on stochastic matching and contention resolution without obvious omissions or self-referential loops. The patience-at-least-2 restriction is a limitation but is handled transparently rather than hidden. The ratios remain well below 1, as is typical for these problems, but the gains are incremental and verifiable in principle. This work is aimed at people already working on stochastic combinatorial optimization and online algorithms; a reader outside that subfield will mostly see the ratio numbers and the standard setup. It is solid enough on its own terms to merit a serious referee, even if the improvements are not paradigm-shifting.

Referee Report

0 major / 3 minor

Summary. The paper introduces new ordered contention resolution schemes (OCRS) for offline stochastic matching. It claims a 0.382-approximation algorithm for general graphs when every vertex has patience at least 2 (improving Baveja et al. 2018's 0.31), a 0.432-approximate random-order probing algorithm without patience constraints (with corollaries including an improved guarantee for Prophet Secretary under edge arrivals), and a 0.632-approximation for bipartite graphs with unit patience on one side (improving Hikima et al. 2021's 1/3). All results assume independent edge realizations and irrevocable matching on successful probes.

Significance. If the derivations hold, the results advance approximation algorithms for stochastic matching by providing the first constant-factor improvements under the stated patience regimes using new OCRS constructions. The explicit algorithmic schemes and analysis for the patience-2 case and the random-order result are strengths; the latter may apply more broadly to prophet inequalities. These are concrete, falsifiable improvements over prior work under standard modeling assumptions.

minor comments (3)

[§3] §3: the formal definition of an ordered CRS could be clarified with an explicit pseudocode listing the probe order and acceptance rule to aid reproducibility of the 0.382 construction.
The analysis of the 0.432 random-order algorithm references several corollaries; a short table summarizing the derived ratios for each corollary would improve readability.
[Preliminaries] Notation for patience parameters (e.g., distinction between per-vertex and global constraints) is consistent but could be introduced earlier with a dedicated preliminary subsection.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation of minor revision. The report does not list any specific major comments to address.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central contribution consists of explicit new ordered contention resolution scheme constructions that directly establish the stated approximation ratios (0.382 under patience >=2, 0.432 without patience constraints, 0.632 for the bipartite unit-patience case) from the standard modeling assumptions of independent edge realizations and irrevocable matching. These constructions improve upon external prior results (Baveja et al. 2018; Hikima et al. 2021) without any reduction of the claimed guarantees to self-definitions, fitted inputs renamed as predictions, or load-bearing self-citations. The derivation chain is therefore self-contained algorithmic analysis rather than circular.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on abstract; central claims rest on standard stochastic matching model assumptions whose details are not expanded here.

axioms (2)

domain assumption Edge existences are independent with known probabilities
Core modeling assumption stated in the abstract for the stochastic setting.
domain assumption Patience constraints limit the number of probes per vertex
Explicitly invoked for the 0.382 guarantee and the bipartite case.

pith-pipeline@v0.9.0 · 5793 in / 1220 out tokens · 36749 ms · 2026-05-24T13:51:06.984546+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages · 1 internal anchor

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Algorithmica 82(1):64–87

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Available at SSRN 3443109

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Gandhi R, Khuller S, Parthasarathy S, Srinivasan A (2006) Dep endent rounding and its applications to approximation algorithms. Journal of the ACM (JACM) 53(3):324–360

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Hikima Y, Akagi Y, Kim H, Kohjima M, Kurashima T, Toda H (2021) In tegrated optimization of bipartite matching and its stochastic behavior: New formulation and approximation algorithm via min- cost ﬂow optimization. The Thirty-Fifth AAAI Conference on Artiﬁcial Intelligenc e, AAAI 2021

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Lee E, Singla S (2018) Optimal online contention resolution schem es via ex-ante prophet inequalities. 26th Annual European Symposium on Algorithms (ESA 2018) (Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik)

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Nanda V, Xu P, Sankararaman KA, Dickerson JP, Srinivasan A (2 020) Balancing the tradeoﬀ between proﬁt and fairness in rideshare platforms during high-demand hour s. The Thirty-Fourth AAAI Con- ference on Artiﬁcial Intelligence, AAAI 2020, The Thirty-S econd Innovative Applications of Artiﬁcial Intelligence Conference, IAAI 2020, The Tenth AAAI Symposi um...

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Xu P, Shi Y, Cheng H, Dickerson JP, Sankararaman KA, Srinivas an A, Tong Y, Tsepenekas L (2019) A uniﬁed approach to online matching with conﬂict-aware constraints . The Thirty-Third AAAI Conference on Artiﬁcial Intelligence, AAAI 2019, The Thirty-First Inn ovative Applications of Artiﬁcial Intelligence Conference, IAAI 2019, The Ninth AAAI Symposium on E...

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[1] [1]

Algorithms-ESA 2015 , 1–12 (Springer)

Adamczyk M, Grandoni F, Mukherjee J (2015) Improved appro ximation algorithms for stochastic matching. Algorithms-ESA 2015 , 1–12 (Springer)

work page 2015

[2] [2]

2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) , 790–801 (IEEE)

Adamczyk M, W/suppress lodarczyk M (2018) Random order contention resolution schemes. 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) , 790–801 (IEEE)

work page 2018

[3] [3]

Bessiere C, ed., Proceedings of the Twenty-Ninth International Joint Confe rence on Artiﬁcial Intelligence, IJCAI 2020 , 3–9 (ijcai.org)

Ahmadi S, Ahmed F, Dickerson JP, Fuge M, Khuller S (2020) An algo rithm for multi-attribute diverse matching. Bessiere C, ed., Proceedings of the Twenty-Ninth International Joint Confe rence on Artiﬁcial Intelligence, IJCAI 2020 , 3–9 (ijcai.org)

work page 2020

[4] [4]

Sierra C, ed., Proceedings of the Twenty-Sixth International Joint Conference on Arti ﬁcial Intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017 , 35–41 (ijcai.org)

Ahmed F, Dickerson JP, Fuge M (2017) Diverse weighted bipartite b-matching. Sierra C, ed., Proceedings of the Twenty-Sixth International Joint Conference on Arti ﬁcial Intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017 , 35–41 (ijcai.org)

work page 2017

[5] [5]

Antoniadis A, Gouleakis T, Kleer P, Kolev P (2020) Secretary and o nline matching problems with machine learned advice. Larochelle H, Ranzato M, Hadsell R, Balcan M F, Lin H, eds., Advances in Neural Information Processing Systems , volume 33, 7933–7944 (Curran Associates, Inc.), URL https://proceedings.neurips.cc/paper/2020/file/5a378f8490c8d6af8647a7538...

work page 2020

[6] [6]

Algorithmica 63(4):733–762

Bansal N, Gupta A, Li J, Mestre J, Nagarajan V, Rudra A (2012 ) When lp is the cure for your matching woes: Improved bounds for stochastic matchings. Algorithmica 63(4):733–762

work page 2012

[7] [7]

Algorithmica 80(11):3225–3252

Baveja A, Chavan A, Nikiforov A, Srinivasan A, Xu P (2018) Impro ved bounds in stochastic matching and optimization. Algorithmica 80(11):3225–3252

work page 2018

[8] [8]

CoRR abs/2102.04325, URL https://arxiv.org/abs/2102.04325

Borodin A, MacRury C, Rakheja A (2021) Prophet inequality matc hing meets probing with commit- ment. CoRR abs/2102.04325, URL https://arxiv.org/abs/2102.04325

work page arXiv 2021

[9] [9]

Brubach B, Grammel N, Ma W, Srinivasan A (2021) Follow your star : New frameworks for online stochastic matching with known and unknown patience. Ba nerjee A, Fukumizu K, eds., Proceedings of The 24th International Conference on Artiﬁc ial Intelligence and Statis- tics, volume 130 of Proceedings of Machine Learning Research , 2872–2880 (PMLR), URL http://...

work page 2021

[10] [10]

Advances in Neural Information Processing Systems 34

Brubach B, Grammel N, Ma W, Srinivasan A (2021) Improved gua rantees for oﬄine stochastic matching via new ordered contention resolution schemes. Advances in Neural Information Processing Systems 34. 16

work page 2021

[11] [11]

Algorithmica 82(1):64–87

Brubach B, Sankararaman KA, Srinivasan A, Xu P (2020) Atten uate locally, win globally: Attenuation- based frameworks for online stochastic matching with timeouts. Algorithmica 82(1):64–87

work page 2020

[12] [12]

Mathematical Programming 1–51

Bruggmann S, Zenklusen R (2020) An optimal monotone conten tion resolution scheme for bipartite matchings via a polyhedral viewpoint. Mathematical Programming 1–51

work page 2020

[13] [13]

Proceedings of the twenty-ninth annual acm-siam symposium on discrete algorithms , 700–714 (SIAM)

Ehsani S, Hajiaghayi M, Kesselheim T, Singla S (2018) Prophet s ecretary for combinatorial auctions and matroids. Proceedings of the twenty-ninth annual acm-siam symposium on discrete algorithms , 700–714 (SIAM)

work page 2018

[14] [14]

SIAM Journal on Discrete Mathematics 31(3):1685–1701

Esfandiari H, Hajiaghayi M, Liaghat V, Monemizadeh M (2017) P rophet secretary. SIAM Journal on Discrete Mathematics 31(3):1685–1701

work page 2017

[15] [15]

Esfandiari H, Korula N, Mirrokni V (2016) Bi-objective online ma tching and submod- ular allocations. Lee D, Sugiyama M, Luxburg U, Guyon I, Garnett R, eds., Advances in Neural Information Processing Systems , volume 29 (Curran Associates, Inc.), URL https://proceedings.neurips.cc/paper/2016/file/0966289037ad9846c5e994be2a91bafa-Paper.pdf

work page arXiv 2016

[16] [16]

Proceedings of the 21st ACM Conference on Economics and Computation, 769–787

Ezra T, Feldman M, Gravin N, Tang ZG (2020) Online stochastic ma x-weight matching: prophet inequal- ity for vertex and edge arrival models. Proceedings of the 21st ACM Conference on Economics and Computation, 769–787

work page 2020

[17] [17]

Available at SSRN 3443109

Fata E, Ma W, Simchi-Levi D (2019) Multi-stage and multi-custom er assortment optimization with inventory constraints. Available at SSRN 3443109

work page 2019

[18] [18]

Journal of the ACM (JACM) 53(3):324–360

Gandhi R, Khuller S, Parthasarathy S, Srinivasan A (2006) Dep endent rounding and its applications to approximation algorithms. Journal of the ACM (JACM) 53(3):324–360

work page 2006

[19] [19]

Proceedings of the 2019 ACM Conference on Economics and Comp utation, 93–109

Gravin N, Wang H (2019) Prophet inequality for bipartite matchin g: merits of being simple and non adaptive. Proceedings of the 2019 ACM Conference on Economics and Comp utation, 93–109

work page 2019

[20] [20]

Understanding the Correlation Gap for Matchings

Guruganesh G, Lee E (2017) Understanding the correlation ga p for matchings. arXiv preprint arXiv:1710.06339

work page internal anchor Pith review Pith/arXiv arXiv 2017

[21] [21]

The Thirty-Fifth AAAI Conference on Artiﬁcial Intelligenc e, AAAI 2021

Hikima Y, Akagi Y, Kim H, Kohjima M, Kurashima T, Toda H (2021) In tegrated optimization of bipartite matching and its stochastic behavior: New formulation and approximation algorithm via min- cost ﬂow optimization. The Thirty-Fifth AAAI Conference on Artiﬁcial Intelligenc e, AAAI 2021

work page 2021

[22] [22]

26th Annual European Symposium on Algorithms (ESA 2018) (Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik)

Lee E, Singla S (2018) Optimal online contention resolution schem es via ex-ante prophet inequalities. 26th Annual European Symposium on Algorithms (ESA 2018) (Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik)

work page 2018

[23] [23]

Nanda V, Xu P, Sankararaman KA, Dickerson JP, Srinivasan A (2 020) Balancing the tradeoﬀ between proﬁt and fairness in rideshare platforms during high-demand hour s. The Thirty-Fourth AAAI Con- ference on Artiﬁcial Intelligence, AAAI 2020, The Thirty-S econd Innovative Applications of Artiﬁcial Intelligence Conference, IAAI 2020, The Tenth AAAI Symposi um...

work page 2020

[24] [24]

Xu P, Shi Y, Cheng H, Dickerson JP, Sankararaman KA, Srinivas an A, Tong Y, Tsepenekas L (2019) A uniﬁed approach to online matching with conﬂict-aware constraints . The Thirty-Third AAAI Conference on Artiﬁcial Intelligence, AAAI 2019, The Thirty-First Inn ovative Applications of Artiﬁcial Intelligence Conference, IAAI 2019, The Ninth AAAI Symposium on E...

work page 2019