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Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms [article]

Moab Arar, Shiri Chechik, Sarel Cohen, Cliff Stein, David Wajc
2018 arXiv   pre-print
We present a simple randomized reduction from fully-dynamic integral matching algorithms to fully-dynamic "approximately-maximal" fractional matching algorithms.  ...  For the (2+ϵ)-approximation regime only a fractional fully-dynamic (2+ϵ)-matching algorithm with worst-case polylog update time was previously known, due to Bhattacharya et al. (SODA 2017).  ...  The fifth author wishes to thank Seffi Naor for a remark which inspired Definition 1.1.  ... 
arXiv:1711.06625v2 fatcat:ibtgntip25dbretoruaww7nqby

Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms

Moab Arar, Shiri Chechik, Sarel Cohen, Cliff Stein, David Wajc, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
We present a simple randomized reduction from fully-dynamic integral matching algorithms to fully-dynamic "approximately-maximal" fractional matching algorithms.  ...  Applying this reduction to the recent fractional matching algorithm of Bhattacharya, Henzinger, and Nanongkai (SODA 2017), we obtain a novel result for the integral problem.  ...  The fifth author wishes to thank Seffi Naor for a remark which inspired Definition 1.1.  ... 
doi:10.4230/lipics.icalp.2018.7 dblp:conf/icalp/ArarCCSW18 fatcat:5sw6c6dv5ve5jfvkp7l6w3b2pi

Dynamic Matching Market Design

Mohammad Akbarpour, Shengwu Li, Shayan Oveis Gharan
2014 Social Science Research Network  
We also show that naïve local algorithms that maintain market thickness by choosing the right time to match agents, but do not exploit global network structure, can perform very close to optimal algorithms  ...  We introduce a simple benchmark model of dynamic matching in networked markets, where agents arrive and depart stochastically and the network of acceptable transactions among agents forms a random graph  ...  This will enable us to investigate whether timing is an important feature of dynamic matching algorithms.  ... 
doi:10.2139/ssrn.2394319 fatcat:td62ktorlvgkbdc3xd2xbles5y

Dynamic Matching Market Design [article]

Mohammad Akbarpour and Shengwu Li and Shayan Oveis Gharan
2014 arXiv   pre-print
From an optimization perspective, naive local algorithms, that choose the right time to match agents but do not exploit global network structure, can perform very close to optimal algorithms.  ...  To elicit agents' departure times, we design an incentive-compatible continuous-time dynamic mechanism without transfers.  ...  Value of Waiting What are the advantages of waiting to thicken the market, compared to implementing 'static maximal' matches via the Greedy Algorithm?  ... 
arXiv:1402.3643v1 fatcat:t7tohjtgwndkjamtk2tivhqpni

Dynamic Algorithms for Maximum Matching Size [article]

Soheil Behnezhad
2022 arXiv   pre-print
We study fully dynamic algorithms for maximum matching. This is a well-studied problem, known to admit several update-time/approximation trade-offs.  ...  For instance, it is known how to maintain a 1/2-approximate matching in (polylog n) time or a 2/3-approximate matching in O(√(n)) time, where n is the number of vertices.  ...  The algorithm of [20] maintains a fractional matching, but not an integral one.  ... 
arXiv:2207.07607v1 fatcat:blj7bsnh5vdqdidpbldxjh3ai4

Dynamic Matching with Better-than-2 Approximation in Polylogarithmic Update Time [article]

Sayan Bhattacharya, Peter Kiss, Thatchaphol Saranurak, David Wajc
2022 arXiv   pre-print
Our algorithms are based on simulating new two-pass streaming matching algorithms in the dynamic setting.  ...  We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better  ...  ], the dynamic fractional matching of [BHN17] is precisely such an approximately-maximal matching.  ... 
arXiv:2207.07438v1 fatcat:bwmc6ces35dzfpsvfnw2hxdfz4

Fully Dynamic Matching in Bipartite Graphs [article]

Aaron Bernstein, Cliff Stein
2015 arXiv   pre-print
Existing algorithms for dynamic matching (in general graphs) seem to fall into two groups: there are fast (mostly randomized) algorithms that do not achieve a better than 2-approximation, and there slow  ...  Our main result is a fully dynamic algorithm that maintains a 3/2 + approximation in worst-case update time O(m^1/4^/2.5).  ...  Acknowledgements We would like to thank Tsvi Kopelowitz for very helpful pointers about dynamic orientations.  ... 
arXiv:1506.07076v2 fatcat:dfu2nrg3yncwffu6srf5bhts5m

Regularized Box-Simplex Games and Dynamic Decremental Bipartite Matching [article]

Arun Jambulapati, Yujia Jin, Aaron Sidford, Kevin Tian
2022 arXiv   pre-print
a (fractional) ϵ-approximate maximum matching in a dynamic decremental bipartite graph against an adaptive adversary.  ...  We give a generic framework which reduces this dynamic matching problem to solving regularized graph-structured optimization problems to high accuracy.  ...  We thank anonymous reviewers for their feedback, Amin Saberi and David Wajc for helpful conversations, Jason Altschuler for providing a reference for the unaccelerated convergence rate of Sinkhorn's algorithm  ... 
arXiv:2204.12721v3 fatcat:qe65bhaeordnjhrsl77v5fywoi

Dynamic Load Balancing by Random Matchings

Bhaskar Ghosh, S. Muthukrishnan
1996 Journal of computer and system sciences (Print)  
The running time of our algorithm is related to the eigenstructure of the underlying graph. We also present experimental results analyzing issues in load balancing related to our algorithms. ]  ...  We present an efficient local algorithm for the dynamic load balancing problem under our model of load movement. Our algorithm works on networks of arbitrary topology under possible failure of links.  ...  DistributedÂParallel algorithms for determining the maximal [II86, L86] matchings of a given graph work by iteratively adding a random matching to a current matching.  ... 
doi:10.1006/jcss.1996.0075 fatcat:e2p66i7im5gcbjwy6ectmoxlnq

Fully Dynamic Almost-Maximal Matching: Breaking the Polynomial Barrier for Worst-Case Time Bounds [article]

Moses Charikar, Shay Solomon
2018 arXiv   pre-print
We present a randomized algorithm for maintaining an almost-maximal matching in fully dynamic graphs with polylogarithmic worst-case update time.  ...  s result) and the first (2+ϵ)-approximation for maximum (integral) matching.  ...  The second author is grateful to Danupon Nanongkai and Uri Zwick for their suggestion to study dynamic matchings in the offline model.  ... 
arXiv:1711.06883v2 fatcat:qzrohakqcbcg5kv6lfnxi22vhq

New Trade-Offs for Fully Dynamic Matching via Hierarchical EDCS [article]

Soheil Behnezhad, Sanjeev Khanna
2022 arXiv   pre-print
Our main contribution is a new approach to designing fully dynamic approximate matching algorithms that in a unified manner not only (essentially) recovers all previously known trade-offs that were achieved  ...  We study the maximum matching problem in fully dynamic graphs: a graph is undergoing both edge insertions and deletions, and the goal is to efficiently maintain a large matching after each edge update.  ...  Does there exist a fully dynamic algorithm maintaining a ( 2 3 +Ω(1))-approximate maximum matching in o(n) update-time?  ... 
arXiv:2201.02905v1 fatcat:3xfdz7j4u5ealfwsqkliaagg5e

Deterministic Dynamic Matching in O(1) Update Time

Sayan Bhattacharya, Deeparnab Chakrabarty, Monika Henzinger
2019 Algorithmica  
Our result can be generalized to give a fully dynamic O( f 3 )-approximate algorithm with O( f 2 ) amortized update time for the hypergraph vertex cover and fractional hypergraph matching problem, where  ...  We present a new deterministic fully dynamic algorithm that maintains a O(1)-approximate minimum vertex cover and maximum fractional matching, with an amortized update time of O(1).  ...  Note that any fractional matching algorithm solves the value version of the dynamic matching problem while degrading the approximation ratio by a factor of 3/2 [8] .  ... 
doi:10.1007/s00453-019-00630-4 fatcat:vqgsq4gghjablm43jzq75nlho4

New deterministic approximation algorithms for fully dynamic matching

Sayan Bhattacharya, Monika Henzinger, Danupon Nanongkai
2016 Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2016  
We present two deterministic dynamic algorithms for the maximum matching problem. (1) An algorithm that maintains a (2+ε)-approximate maximum matching in general graphs with O(poly(log n, 1/ε)) update  ...  time for the dynamic maximum-weight matching problem, where W is the ratio between the largest and smallest edge weights. 3 We can actually maintain an approximate fractional matching with the same performance  ...  The value of a λ -maximal fractional matching in G is a 2λ -approximation to OPT f G .  ... 
doi:10.1145/2897518.2897568 dblp:conf/stoc/BhattacharyaHN16 fatcat:2njvhjmcbzfwzddpc5r7xoo5zm

New Deterministic Approximation Algorithms for Fully Dynamic Matching [article]

Sayan Bhattacharya and Monika Henzinger and Danupon Nanongkai
2016 arXiv   pre-print
We present two deterministic dynamic algorithms for the maximum matching problem. (1) An algorithm that maintains a (2+ϵ)-approximate maximum matching in general graphs with O(poly( n, 1/ϵ)) update time  ...  Its approximation guarantee almost matches the guarantee of the best randomized polylogarithmic update time algorithm [Baswana et al. FOCS 2011].  ...  The value of a λ -maximal fractional matching in G is a 2λ -approximation to OPT f G .  ... 
arXiv:1604.05765v1 fatcat:lkhxjtmyhnd7bp74kyw7n6nhpu

Fully Dynamic Matching: Beating 2-Approximation in Δ^ϵ Update Time [article]

Soheil Behnezhad, Jakub Łącki, Vahab Mirrokni
2019 arXiv   pre-print
In fully dynamic graphs, we know how to maintain a 2-approximation of maximum matching extremely fast, that is, in polylogarithmic update time or better.  ...  Previously, the fastest fully dynamic matching algorithm providing a better-than-2 approximation had O(m^1/4) update-time [Bernstein and Stein, SODA 2016].  ...  Acknowledgements Soheil Behnezhad thanks Mahsa Derakhshan, MohammadTaghi Hajiaghayi, Cliff Stein and Madhu Sudan for their collaboration in [6] and Sepehr Assadi for many helpful discussions and pointers to  ... 
arXiv:1911.01839v1 fatcat:cx76uc4ljregzoz65fpmh3lvfa
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