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How to Match when All Vertices Arrive Online [article]

Zhiyi Huang, Ning Kang, Zhihao Gavin Tang, Xiaowei Wu, Yuhao Zhang and Xue Zhu
2018 arXiv   pre-print
We introduce a fully online model of maximum cardinality matching in which all vertices arrive online. On the arrival of a vertex, its incident edges to previously-arrived vertices are revealed.  ...  Each vertex has a deadline that is after all its neighbors' arrivals.  ...  Wang and Wong [WW15] considered a more restrictive model of online bipartite matching with both sides of vertices arriving online: A vertex can only actively match other vertices at its arrival; if it  ... 
arXiv:1802.03905v1 fatcat:lyyuzrccvjenvllahxxiyiclri

Online Vertex-Weighted Bipartite Matching and Single-bid Budgeted Allocations [article]

Gagan Aggarwal, Gagan Goel, Chinmay Karande, Aranyak Mehta
2010 arXiv   pre-print
The vertices in U have weights and are known ahead of time, while the vertices in V arrive online in an arbitrary order and have to be matched upon arrival.  ...  When all the weights are equal, this reduces to the classic online bipartite matching problem for which Karp, Vazirani and Vazirani gave an optimal (1-1/e)-competitive algorithm in their seminal work KVV90  ...  Vertices in V arrive one at a time, online, revealing their incident edges. An arriving vertex can be matched to an unmatched neighbor upon arrival.  ... 
arXiv:1007.1271v1 fatcat:cl34rdzqmvcivce5iysrxkitae

Bayesian Mechanism Design

Aranyak Mehta
2013 Foundations and Trends® in Theoretical Computer Science  
on how many vertices v ∈ V can be matched to u.  ...  Online matching with edge arrivals: Edges of the graph arrive online, and an arriving edge can be selected in the matching when it arrives.  ... 
doi:10.1561/0400000057 fatcat:a7zzdglqmndh3bwdcxiklxoicu

Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals

Zhiyi Huang, Zhihao Gavin Tang, Xiaowei Wu, Yuhao Zhang, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
(STOC 1990), and prove a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order.  ...  Our algorithm has a natural interpretation that offline vertices offer a larger portion of their weights to the online vertices as time goes by, and each online vertex matches the neighbor with the highest  ...  Acknowledgements The first author would like to thank Nikhil Devanur, Ankit Sharma, and Mohit Singh with whom he made an initial attempt to reproduce the results of Mahdian and Yan using the randomized  ... 
doi:10.4230/lipics.icalp.2018.79 dblp:conf/icalp/0002TWZ18 fatcat:jh5owerumzhg3lkmt672c65mtm

Edge Weighted Online Windowed Matching

Itai Ashlagi, Maximilien Burq, Chinmoy Dutta, Patrick Jaillet, Amin Saberi, Chris Sholley
2019 Proceedings of the 2019 ACM Conference on Economics and Computation - EC '19  
When the arrival order is chosen uniformly at random, we show that a batching algorithm, which computes a maximum-weighted matching every (d + 1) periods, is 0.279-competitive.  ...  Each pair of agents can yield a different match value, and the planner's goal is to maximize the total value over a finite time horizon.  ...  After the first two arrivals, the online algorithm A needs to decide whether to match them or let the first arrival leave.  ... 
doi:10.1145/3328526.3329573 dblp:conf/ec/AshlagiBDJSS19 fatcat:uzevnr2hqrhollee7ian4s6oa4

Online Primal Dual Meets Online Matching with Stochastic Rewards: Configuration LP to the Rescue [article]

Zhiyi Huang, Qiankun Zhang
2020 arXiv   pre-print
Our results further generalize to the vertex-weighted case due to the intrinsic robustness of the randomized online primal dual analysis.  ...  This paper unlocks the power of randomized online primal dual in online matching with stochastic rewards by employing the configuration linear program rather than the standard matching linear program used  ...  [14, 16] that consider a generalization of online bipartite matching called fully online matching, where the graph is not necessarily bipartite and all vertices arrive online.  ... 
arXiv:2002.01802v1 fatcat:5odr7ts7mjbz3bbafcmq4oplly

Maximum Weight Online Matching with Deadlines [article]

Itai Ashlagi, Maximilien Burq, Chinmoy Dutta, Patrick Jaillet, Amin Saberi, Chris Sholley
2018 arXiv   pre-print
When the arrival order is chosen uniformly at random, we show that a batching algorithm, which computes a maximum-weighted matching every (d+1) periods, is 0.279-competitive.  ...  We study the problem of matching agents who arrive at a marketplace over time and leave after d time periods. Agents can only be matched while they are present in the marketplace.  ...  Third, all vertices can arrive over time and may remain for some given time until they are matched.  ... 
arXiv:1808.03526v1 fatcat:okg5viadczhqjp3cfpetgjwqle

Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals [article]

Zhiyi Huang, Zhihao Gavin Tang, Xiaowei Wu, Yuhao Zhang
2019 arXiv   pre-print
(STOC 1990), and prove a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order.  ...  Our algorithm has a natural interpretation that offline vertices offer a larger portion of their weights to the online vertices as time goes by, and each online vertex matches the neighbor with the highest  ...  ACKNOWLEDGEMENTS The first author would like to thank Nikhil Devanur, Ankit Sharma, and Mohit Singh with whom he made an initial attempt to reproduce the results of Mahdian and Yan using the randomized  ... 
arXiv:1804.07458v2 fatcat:rc3pesiodbf4fdoujz2kppq2jy

Online minimum matching with uniform metric and random arrivals [article]

Sharmila Duppala, Karthik A. Sankararaman, Pan Xu
2021 arXiv   pre-print
We consider Online Minimum Bipartite Matching under the uniform metric. We show that Randomized Greedy achieves a competitive ratio equal to (1+1/n) (H_n+1-1), which matches the lower bound.  ...  Comparing with the fact that RG achieves an optimal ratio of Θ(ln n) for the same problem but under the adversarial order, we find that the weaker arrival assumption of random order doesn't offer any extra  ...  Points in are known in advance while points in arrive sequentially in an online fashion: upon the arrival of each ∈ , we have to match it with a point ∈ , and it incurs a cost of .  ... 
arXiv:2112.05247v1 fatcat:4ilf72rrkzfghdu37op3qah34e

Online Graph Matching Problems with a Worst-Case Reassignment Budget [article]

Yongho Shin, Kangsan Kim, Seungmin Lee, Hyung-Chan An
2020 arXiv   pre-print
The algorithm is required to maintain a matching in the current graph, where the algorithm revises the matching after each vertex arrival by reassigning vertices.  ...  In the online bipartite matching with reassignments problem, an algorithm is initially given only one side of the vertex set of a bipartite graph; the vertices on the other side are revealed to the algorithm  ...  For all constant > 0, no deterministic algorithm is ( 1 2 + )-competitive for the maximumweight online bipartite left-perfect matching problem under vertex arrivals with k = 4, even when all edge weights  ... 
arXiv:2003.05175v1 fatcat:bgkgfcoxjvgtdnnzr2fugavpwu

Online Vertex Cover and Matching: Beating the Greedy Algorithm [article]

Yajun Wang, Sam Chiu-wai Wong
2013 arXiv   pre-print
When a vertex arrives, all its incident edges to previously arrived vertices are revealed to the algorithm.  ...  In the online vertex cover problem, we are required to maintain a monotone vertex cover in a graph whose vertices arrive online.  ...  When an online vertex v arrives, all of its edges incident to the previously arrived vertices are revealed.  ... 
arXiv:1305.1694v1 fatcat:f6wim7bkkng33g7o2xlc6wtdde

Online mobile Micro-Task Allocation in spatial crowdsourcing

Yongxin Tong, Jieying She, Bolin Ding, Libin Wang, Lei Chen
2016 2016 IEEE 32nd International Conference on Data Engineering (ICDE)  
We first extend the state-of-art algorithm for the online maximum weighted bipartite matching problem to the GOMA problem as the baseline algorithm.  ...  Most existing studies focus on offline scenarios, where all the spatiotemporal information of microtasks and crowd workers is given.  ...  However, all these existing studies only address the case where one single side of vertices arrive online.  ... 
doi:10.1109/icde.2016.7498228 dblp:conf/icde/TongSDWC16 fatcat:nakbsec2wbchtoqlkzbbc7empu

Follow Your Star: New Frameworks for Online Stochastic Matching with Known and Unknown Patience [article]

Brian Brubach, Nathaniel Grammel, Will Ma, Aravind Srinivasan
2021 arXiv   pre-print
We then build a framework which uses these star graph algorithms as black boxes to solve the online matching problems under different arrival settings.  ...  Our approach to online matching utilizes black-box algorithms for matching on star graphs under various models of patience.  ...  relevant to this paper.  ... 
arXiv:1907.03963v3 fatcat:mujhjz7afvf6hm4e5eaiwabkdq

Fully Online Matching II: Beating Ranking and Water-filling [article]

Zhiyi Huang, Zhihao Gavin Tang, Xiaowei Wu, Yuhao Zhang
2020 arXiv   pre-print
(STOC 2018, SODA 2019) introduced a more general model called fully online matching, which considers general graphs and allows all vertices to arrive online.  ...  Our result for fractional matching further shows a separation between fully online matching and the general vertex arrival model by Wang and Wong (ICALP 2015), due to an upper bound of 0.5914 in the latter  ...  a b-matching problem in which online vertices arrive in batches of b copies and b tends to infinity.  ... 
arXiv:2005.06311v1 fatcat:pmhwnckaebe5vfkwbmg5hrczaa

Improved Bounds for Fractional Online Matching Problems [article]

Zhihao Gavin Tang, Yuhao Zhang
2022 arXiv   pre-print
all vertices to arrive online.  ...  Namely, online matching with general vertex arrival is introduced by Wang and Wong (ICALP 2015), and fully online matching is introduced by Huang et al. (JACM 2020).  ...  The one-sided arrival model is a special case when offline vertices all arrive before online vertices. Fully Online Matching. Huang et al. [19] proposed the fully online matching problem.  ... 
arXiv:2202.02948v2 fatcat:jaqpjwyafvgahfd752mrigzhsa
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