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Nearly Optimal Communication and Query Complexity of Bipartite Matching [article]

Joakim Blikstad, Jan van den Brand, Yuval Efron, Sagnik Mukhopadhyay, Danupon Nanongkai
2022 arXiv   pre-print
We also settle the communication complexity of the generalizations of BMM, such as maximum-cost bipartite b-matching and transshipment; and the query complexity of unique bipartite perfect matching (answering  ...  We settle the complexities of the maximum-cardinality bipartite matching problem (BMM) up to poly-logarithmic factors in five models of computation: the two-party communication, AND query, OR query, XOR  ...  The authors would like to thank Gal Beniamini for fruitful discussions and anonymous reviewers of FOCS 2022 for their useful suggestions.  ... 
arXiv:2208.02526v1 fatcat:pvw57rx2dbhr7huwkxkt4wwiuy

New bounds on the classical and quantum communication complexity of some graph properties

Gábor Ivanyos, Hartmut Klauck, Troy Lee, Miklos Santha, Ronald De Wolf, Marc Herbstritt
2012 Foundations of Software Technology and Theoretical Computer Science  
Our main results are: An Ω(n) lower bound on the quantum communication complexity of deciding whether an nvertex graph G is connected, nearly matching the trivial classical upper bound of O(n log n) bits  ...  A deterministic upper bound of O(n 3/2 log n) bits for deciding if a bipartite graph contains a perfect matching, and a quantum lower bound of Ω(n) for this problem.  ...  For Bipartite Matching, can we show that the deterministic O(n 3/2 log n)-bit protocol is essentially optimal, for instance by means of a 2 Ω(n 3/2 ) lower bound on the rank of the associated communication  ... 
doi:10.4230/lipics.fsttcs.2012.148 dblp:conf/fsttcs/IvanyosKLSW12 fatcat:ennhzrejhjbjbhhlotzqkrktwu

New bounds on the classical and quantum communication complexity of some graph properties [article]

Gabor Ivanyos, Hartmut Klauck, Troy Lee, Miklos Santha, Ronald de Wolf
2012 arXiv   pre-print
Our main results are: * An Omega(n) lower bound on the quantum communication complexity of deciding whether an n-vertex graph G is connected, nearly matching the trivial classical upper bound of O(n log  ...  n) bits of communication. * A deterministic upper bound of O(n^3/2log n) bits for deciding if a bipartite graph contains a perfect matching, and a quantum lower bound of Omega(n) for this problem. * A  ...  Our main results are: • An Ω(n) lower bound on the quantum communication complexity of deciding whether G is connected, nearly matching the trivial classical upper bound of O(n log n) bits. • Hajnal et  ... 
arXiv:1204.4596v1 fatcat:3cui5wdo7bekzokvakb3xwvihe

Theoretical Foundations of Storage Systems (Dagstuhl Seminar 19111)

Martin Farach-Colton, Inge Li Gørtz, Rob Johnson, Donald E. Porter, Michael Wagner
2019 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 19111 "Theoretical Foundations of Storage Systems."  ...  This seminar brought together researchers from two distinct communities -algorithms researchers with an interest in external memory and systems researchers with an interest in storage -with the objective  ...  Holmm, Eva Rotenberg In this talk, we introduce the online with recourse model, and give an example: online bipartite matchings.  ... 
doi:10.4230/dagrep.9.3.39 dblp:journals/dagstuhl-reports/Farach-ColtonGJ19 fatcat:pfbfw7sgzjeq7eoqnjurmwzq5u

Independent Set, Induced Matching, and Pricing: Connections and Tight (Subexponential Time) Approximation Hardnesses [article]

Parinya Chalermsook, Bundit Laekhanukit, Danupon Nanongkai
2013 arXiv   pre-print
This nearly matches the upper bound of 2^n/r (Cygan et al., 2008).  ...  The second is the hardness of approximating the maximum induced matching problem on bounded-degree bipartite graphs.  ...  nearly-linear size and optimal free-bit complexity.  ... 
arXiv:1308.2617v2 fatcat:4xrgaznlkffobhdducjuamwf6i

Independent Set, Induced Matching, and Pricing: Connections and Tight (Subexponential Time) Approximation Hardnesses

Parinya Chalermsook, Bundit Laekhanukit, Danupon Nanongkai
2013 2013 IEEE 54th Annual Symposium on Foundations of Computer Science  
The second is the hardness of approximating the maximum induced matching problem on bounded-degree bipartite graphs.  ...  The first in our series is the subexponential-time inapproximability of the maximum independent set problem, a question studied in the area of parameterized complexity.  ...  nearly-linear size and optimal free-bit complexity.  ... 
doi:10.1109/focs.2013.47 dblp:conf/focs/ChalermsookLN13 fatcat:wvu3lxve3ba7vey7wa6t67mka4

Applications of the Quantum Algorithm for st-Connectivity

Kai DeLorenzo, Shelby Kimmel, R. Teal Witter, Michael Wagner
2019 Theory of Quantum Computation, Communication, and Cryptography  
We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity.  ...  We also provide algorithms for detecting even-length cycles and for estimating the circuit rank of a graph. All of our algorithms have logarithmic space complexity.  ...  Bipartiteness An optimal quantum query algorithm for bipartiteness was created by Ārin , š [2] , matching the lower bound of Ω(n 3/2 ) [19] .  ... 
doi:10.4230/lipics.tqc.2019.6 dblp:conf/tqc/DeLorenzoKW19 fatcat:fhvwz235mncpna6qgq4yw3zg5y

Average-Case Communication Complexity of Statistical Problems [article]

Cyrus Rashtchian, David P. Woodruff, Peng Ye, Hanlin Zhu
2021 arXiv   pre-print
We study statistical problems, such as planted clique, its variants, and sparse principal component analysis in the context of average-case communication complexity.  ...  Many of these results are nearly tight, and we use our techniques to provide simple proofs of some known lower bounds for the edge-probe model.  ...  On the other hand, from a query complexity point of view, our upper and lower bounds for sketching algorithms nearly match for the PPC problem. • Hidden Hubs (HH).  ... 
arXiv:2107.01335v1 fatcat:bq4332fg3ndnfn2j4e5l4c5qne

Nearly Complete Graphs Decomposable into Large Induced Matchings and their Applications [article]

Noga Alon, Ankur Moitra, Benny Sudakov
2011 arXiv   pre-print
This disproves (in a strong form) a conjecture of Meshulam, substantially improves a result of Birk, Linial and Meshulam on communicating over a shared channel, and (slightly) extends the analysis of Håstad  ...  and Wigderson of the graph test of Samorodnitsky and Trevisan for linearity.  ...  Acknowledgment We thank Roy Meshulam and Santosh Vempala for helpful comments.  ... 
arXiv:1111.0253v2 fatcat:vg6tl7fwifdujgsewlufpy6a5e

Closure-Tree: An Index Structure for Graph Queries

Huahai He, A.K. Singh
2006 22nd International Conference on Data Engineering (ICDE'06)  
For similarity queries, our experiments validate the quality and efficiency of the presented algorithms.  ...  For similarity queries, we measure graph similarity through edit distance using heuristic graph mapping methods. We implement two kinds of similarity queries: K-NN query and range query.  ...  Shasha and R. Giugno for sharing the code of GraphGrep, and M. Kuramochi and G. Karypis for providing the synthetic graph generator.  ... 
doi:10.1109/icde.2006.37 dblp:conf/icde/HeS06 fatcat:b6wmoc5yfzfyjdg2vvohzi5zy4

Nearly complete graphs decomposable into large induced matchings and their applications

Noga Alon, Ankur Moitra, Benny Sudakov
2012 Proceedings of the 44th symposium on Theory of Computing - STOC '12  
This disproves (in a strong form) a conjecture of Meshulam, substantially improves a result of Birk, Linial and Meshulam on communicating over a shared channel, and (slightly) extends the analysis of Håstad  ...  and Wigderson of the graph test of Samorodnitsky and Trevisan for linearity.  ...  Acknowledgment We thank Roy Meshulam and Santosh Vempala for helpful comments.  ... 
doi:10.1145/2213977.2214074 dblp:conf/stoc/AlonMS12 fatcat:jddake3xkfh2xmnidtqmcuz5ta

Nearly complete graphs decomposable into large induced matchings and their applications

Noga Alon, Ankur Moitra, Benjamin Sudakov
2013 Journal of the European Mathematical Society (Print)  
This disproves (in a strong form) a conjecture of Meshulam, substantially improves a result of Birk, Linial and Meshulam on communicating over a shared channel, and (slightly) extends the analysis of Håstad  ...  and Wigderson of the graph test of Samorodnitsky and Trevisan for linearity.  ...  Motivated by the problem of designing a PCP with optimal amortized query complexity and the related problem for linearity testing, Samorodnitsky and Trevisan introduced a graph-based linearity test: Associate  ... 
doi:10.4171/jems/398 fatcat:oohcjpjonvepzemkyrc6hxffsu

Sublinear Algorithms for Hierarchical Clustering [article]

Arpit Agarwal, Sanjeev Khanna, Huan Li, Prathamesh Patil
2022 arXiv   pre-print
We complement our algorithmic results by establishing nearly matching lower bounds that rule out the possibility of designing better algorithms in each of these models.  ...  primary resources to optimize: (1) (dynamic) streaming model where edges are presented as a stream, (2) query model where the graph is queried using neighbor and degree queries, (3) MPC model where the  ...  Result 7 shows that the worst-case query complexity of our algorithm is nearly optimal.  ... 
arXiv:2206.07633v1 fatcat:krqszwfpnbfjnny6xflkm5erai

Bayesian Mechanism Design

Aranyak Mehta
2013 Foundations and Trends® in Theoretical Computer Science  
The problem of finding a maximum matching in a graph is a classic one, rich in history and central to algorithms and complexity.  ...  The problem of online matching and allocation has generated a lot of interest in the algorithms community, with the introduction of a large number of new problems, models and algorithmic techniques.  ... 
doi:10.1561/0400000057 fatcat:a7zzdglqmndh3bwdcxiklxoicu

Electronic Markets and Auctions (Dagstuhl Seminar 13461)

Yishay Mansour, Benny Moldovanu, Noam Nisan, Berthold Vöcking, Marc Herbstritt
2014 Dagstuhl Reports  
The recent emergence of electronic markets and auctions has only reemphasized the importance of this topic.  ...  The main goal of this seminar was to study topics related to electronic markets and auctions both from the computational perspective and from a game-theoretic and economic one.  ...  We consider this problem in the framework of simultaneous communication complexity. We analyze the amount of simultaneous communication required for achieving an approximately efficient allocation.  ... 
doi:10.4230/dagrep.3.11.58 dblp:journals/dagstuhl-reports/MansourMNV13 fatcat:yvkfyeeezrhhnhckygpqseqwx4
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