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Limits on Counting Triangles using Bipartite Independent Set Queries [article]

Arijit Bishnu, Arijit Ghosh, Gopinath Mishra
2022 arXiv   pre-print
[ITCS 2018 & TALG 2021] introduced and used the Bipartite Independent Set (BIS) and Independent Set (IS) oracle access to an unknown, simple, unweighted and undirected graph and solved the edge estimation  ...  Syst. 2021], and Chen et al. [SODA 2020]. Edge estimation using BIS can be done using polylogarithmic queries, while IS queries need sub-linear but more than polylogarithmic queries.  ...  One can observe the interest generated in these (bipartite) independent set based oracles in a short span of time.  ... 
arXiv:2110.03836v2 fatcat:leothywjdvdaxpwn5v4wn2gjny

Distance Oracles beyond the Thorup-Zwick Bound

Mihai Patrascu, Liam Roditty
2010 2010 IEEE 51st Annual Symposium on Foundations of Computer Science  
The state of the art in distance oracles can be understood by reference to the landmark result of Thorup and Zwick from STOC'01 [TZ05].  ...  Based on a plausible conjecture about the hardness of set intersection queries, we show that a 2-approximate distance oracle requires space Ω(n 2 / √ α).  ...  In this case, we would obtain space lower bounds against distance oracles with polylogarithmic query time.  ... 
doi:10.1109/focs.2010.83 dblp:conf/focs/PatrascuR10 fatcat:krrgiaeaq5dvdbreosiw7oi6p4

Applications of the Adversary Method in Quantum Query Algorithms [article]

Aleksandrs Belovs
2014 arXiv   pre-print
. * We use learning graphs to improve quantum query complexity of the triangle detection and the k-distinctness problems. * We prove tight lower bounds for the k-sum and the triangle sum problems. * We  ...  properties of a graph and its quantum hitting time.  ...  It is bipartite: The part A contains all V i and Z i for i even, and B contains all V i and Z i for i odd. The support of ς is contained in A.  ... 
arXiv:1402.3858v1 fatcat:etcbmdej4bfxbhieqqfq6wd3lq

Approximating the Simplicial Depth [article]

Peyman Afshani, Donald R. Sheehy, Yannik Stein
2015 arXiv   pre-print
For d=2, we present a new data structure that can approximate the simplicial depth in polylogarithmic time, using polylogarithmic query time.  ...  In 3D, we can approximate the simplicial depth of a given point in near-linear time, which is clearly optimal up to polylogarithmic factors.  ...  This work was initiated while YS was visiting MADALGO in Aarhus. I would like to thank the working group for their hospitality and for a constructive atmosphere.  ... 
arXiv:1512.04856v2 fatcat:k4zrfcgmrvdadpjzmf3rqvckuy

How the Degeneracy Helps for Triangle Counting in Graph Streams [article]

Suman K. Bera, C. Seshadhri
2020 arXiv   pre-print
We revisit the well-studied problem of triangle count estimation in graph streams.  ...  Given a graph represented as a stream of m edges, our aim is to compute a (1±ε)-approximation to the triangle count T, using a small space algorithm.  ...  The authors are supported by NSF TRIPODS grant CCF-1740850, NSF CCF-1813165, CCF-1909790, and ARO Award W911NF1910294.  ... 
arXiv:2003.13151v1 fatcat:woqbbwykzrctllyj73o635lh4u

On the Implementation of Huge Random Objects

Oded Goldreich, Shafi Goldwasser, Asaf Nussboim
2010 SIAM journal on computing (Print)  
We initiate a general study of the feasibility of implementing (huge) random objects, and demonstrate its applicability to a number of areas in which random objects occur naturally.  ...  path in such a graph).  ...  -independent random graphs (i.e., the amount of independence is polylogarithmic in the size of the graph).  ... 
doi:10.1137/080722771 fatcat:g3wehwshdvaetmgpfq6h5656xi

Span Programs and Quantum Algorithms for st-Connectivity and Claw Detection [chapter]

Aleksandrs Belovs, Ben W. Reichardt
2012 Lecture Notes in Computer Science  
All these algorithms can be implemented time efficiently and, except for the triangle-detection algorithm, in logarithmic space.  ...  We also show that if T is a path, a star with two subdivided legs, or a subdivision of a claw, its presence as a subgraph in the input graph G can be detected with O(n) quantum queries to the adjacency  ...  A.B. would like to thank Andrew Childs for hospitality; Andrew Childs, Robin Kothari, and Rajat Mittal for many useful discussions; and Jim Geelen for sharing the example in Figure 3 .  ... 
doi:10.1007/978-3-642-33090-2_18 fatcat:myc3thlt4zambberysbcnj2wra

Finding cycles and trees in sublinear time

Artur Czumaj, Oded Goldreich, Dana Ron, C. Seshadhri, Asaf Shapira, Christian Sohler
2012 Random structures & algorithms (Print)  
This matches the known Ω( √ N ) query lower bound for one-sided error cycle-freeness testing, and contrasts with the fact that any minor-free property admits a two-sided error tester of query complexity  ...  We present sublinear-time (randomized) algorithms for finding simple cycles of length at least k ≥ 3 and tree-minors in bounded-degree graphs.  ...  , corrections, and suggestions.  ... 
doi:10.1002/rsa.20462 fatcat:zcl7kww23nh5lcnqn5bmuagmia

Quantum-accelerated constraint programming

Kyle E. C. Booth, Bryan O'Gorman, Jeffrey Marshall, Stuart Hadfield, Eleanor Rieffel
2021 Quantum  
In this paper, we show how quantum algorithms can accelerate CP, at both the levels of inference and search.  ...  This work suggests that CP is a promising candidate application for early fault-tolerant quantum computers and beyond.  ...  Query complexity counts the number of queries (calls to the oracle) the algorithm uses.  ... 
doi:10.22331/q-2021-09-28-550 fatcat:delihkthejbpfb7iwybs7z7yh4

Quantum-accelerated constraint programming [article]

Kyle E. C. Booth, Bryan O'Gorman, Jeffrey Marshall, Stuart Hadfield, Eleanor Rieffel
2021 arXiv   pre-print
In this paper, we show how quantum algorithms can accelerate CP, at both the levels of inference and search.  ...  This work suggests that CP is a promising candidate application for early fault-tolerant quantum computers and beyond.  ...  Query complexity counts the number of queries (calls to the oracle) the algorithm uses.  ... 
arXiv:2103.04502v2 fatcat:g2a6fu2tt5cdvgvziwdy5tgtla

Finding Cycles and Trees in Sublinear Time [article]

Artur Czumaj and Oded Goldreich and Dana Ron and C. Seshadhri and Asaf Shapira and Christian Sohler
2012 arXiv   pre-print
In particular, if the graph is far (i.e., Ω(1)-far) from being cycle-free, i.e. if one has to delete a constant fraction of edges to make it cycle-free, then the algorithm finds a cycle of polylogarithmic  ...  This matches the known Ω(√(N)) query lower bound, and contrasts with the fact that any minor-free property admits a two-sided error tester of query complexity that only depends on the proximity parameter  ...  Acknowledgments We are grateful to Aviv Reznik for useful comments on a prior version, and to the anonymous reviewers for their comments and suggestions.  ... 
arXiv:1007.4230v3 fatcat:kgohxullizakxlitgdmmz74w2e

Robust Regression Revisited: Acceleration and Improved Estimation Rates [article]

Arun Jambulapati, Jerry Li, Tselil Schramm, Kevin Tian
2021 arXiv   pre-print
Prior works in this line of research were based on the robust gradient descent framework of Prasad et. al., a first-order method using biased gradient queries, or the Sever framework of Diakonikolas et  ...  For the general case of smooth GLMs (e.g. logistic regression), we show that the robust gradient descent framework of Prasad et. al. can be accelerated, and show our algorithm extends to optimizing the  ...  Acknowledgments KT is supported by NSF Grant CCF-1955039 and the Alfred P. Sloan Foundation.  ... 
arXiv:2106.11938v1 fatcat:batr6fo7ybbqrfogkuhmtagx3a

Approximating Edit Distance in Truly Subquadratic Time: Quantum and MapReduce [article]

Mahdi Boroujeni and Soheil Ehsani and Mohammad Ghodsi and MohammadTaghi HajiAghayi and Saeed Seddighin
2018 arXiv   pre-print
For a quantum algorithm, we reduce the black box to metric estimation and provide efficient algorithms for approximating it.  ...  Our solutions are based on a framework for approximating edit distance in parallel settings.  ...  Acknowledgment We would like to thank Andrew Childs, Omid Etesami, Salman Beigi, and Mohammad Ali Abam for their comments on an earlier version of the paper.  ... 
arXiv:1804.04178v2 fatcat:ij3ko4ecvrfexoywajetqvjoj4

Hardness for Triangle Problems under Even More Believable Hypotheses: Reductions from Real APSP, Real 3SUM, and OV [article]

Timothy M. Chan, Virginia Vassilevska Williams, Yinzhan Xu
2022 arXiv   pre-print
The "Real APSP" and "Real 3SUM" hypotheses, which assert that the APSP and 3SUM hypotheses hold for real-valued inputs in a reasonable version of the Real RAM model, are even more believable than their  ...  Our main result is a nontrivial lower bound for a slight generalization of Triangle Collection, called All-Color-Pairs Triangle Collection, under the even more believable hypothesis that at least one of  ...  each i, j ∈ [n], we want to count the number of indices k The overall number of calls to the oracle for Real-Exact-Tri-Variant 3 is polylogarithmic.  ... 
arXiv:2203.08356v2 fatcat:c2t2jzuf6ngbzfdpy7sonn5mzu

On Learning and Testing Dynamic Environments

Oded Goldreich, Dana Ron
2014 2014 IEEE 55th Annual Symposium on Foundations of Computer Science  
one-dimensional movement can be tested within a total number of queries that is independent of the size of the environment.  ...  Specifically, we show that evolution according to any linear rule can be tested within a total number of queries that is sublinear in the size of the environment, and that evolution according to a simple  ...  We note that Theorem 6.7 holds also in a model in which ENV returns the identity of the object residing in the queried location at the queried time (as considered in Section 7.3), but LOC is not available  ... 
doi:10.1109/focs.2014.43 dblp:conf/focs/GoldreichR14 fatcat:yokjzzphuzh3pl3qam7dxndbvm
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