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On Fully Dynamic Graph Sparsifiers

Ittai Abraham, David Durfee, Ioannis Koutis, Sebastian Krinninger, Richard Peng
2016 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)  
Second, we give a fully dynamic algorithm for maintaining a (1 ±ϵ) -cut sparsifier with worst-case update time poly(n, ϵ^-1). Both sparsifiers have size n · poly(n, ϵ^-1).  ...  We initiate the study of dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after  ...  Proof of Theorem 8.10 : Any edge insertion/deletion inG requires O(poly(log n, −1 )) update time for G and VC from Lemma 8.13.  ... 
doi:10.1109/focs.2016.44 dblp:conf/focs/AbrahamDKKP16 fatcat:tu35ze66lncbdbg32fjv63az5u

Quantum Meets the Minimum Circuit Size Problem [article]

Nai-Hui Chia, Chi-Ning Chou, Jiayu Zhang, Ruizhe Zhang
2021 arXiv   pre-print
We discover that some reductions that are not known for classical MCSP exist for quantum MCSPs for unitaries and states, e.g., search-to-decision reduction and self-reduction.  ...  Our findings could be of interest for future studies, and we post several open problems for further exploration along this direction.  ...  Acknowledgment We are grateful to Scott Aaronson  ... 
arXiv:2108.03171v3 fatcat:bgmake6gnrdt3jvrywagxgn4rq

Pattern-Based Approach to the Workflow Satisfiability Problem with User-Independent Constraints [article]

Daniel Karapetyan, Andrew J. Parkes, Gregory Gutin, Andrei Gagarin
2019 arXiv   pre-print
(JAIR 2014) that WSP restricted to the class of user-independent constraints (UI), covering many practical cases, admits FPT algorithms, i.e. can be solved in time exponential only in the number of steps  ...  k and polynomial in the number of users n.  ...  This research was partially supported by EPSRC grants EP/H000968/1 (for DK and AP), EP/K005162/1 (for AG and GG), and a Leverhulme Trust grant (GG).  ... 
arXiv:1604.05636v4 fatcat:r6vtyhuym5b4fbahn3fzrqfafa

Editor: Anna R. Karlin; Article No

Oded Goldreich, Guy Rothblum
19 Leibniz International Proceedings in Informatics Schloss Dagstuhl-Leibniz-Zentrum für Informatik   unpublished
Specifically, such constructions are presented for t-CLIQUE and t-SUM.  ...  We present direct constructions of doubly-efficient interactive proof systems for problems in P that are believed to have relatively high complexity.  ...  Building on the identification of this class and its proof systems, our subsequent work [14] , which also builds on the work of [5] , shows worst-case to average-case reductions between problems in a  ... 

Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches

Graham Cormode
2011 Foundations and Trends in Databases  
They are often the only means of providing interactive response times when exploring massive datasets, and are also needed to handle high speed data streams.  ...  The central difference is that, whereas histograms primarily produce buckets that are subsets of the original data-attribute domain, wavelet representations transform the data and seek to represent the  ...  Acknowledgments The work of Minos Garofalakis was partially supported by the European Commission under FP7-FET Open (Future and Emerging Technologies) ICT-2009.8.0 grant no. 255957 (LIFT).  ... 
doi:10.1561/1900000004 fatcat:wk7razxkmzcv7fzczftlohblwa

Efficiently Finding a Maximal Clique Summary via Effective Sampling [article]

Xiaofan Li, Rui Zhou, Lu Chen, Chengfei Liu, Qiang He, Yun Yang
2020 arXiv   pre-print
under certain optimality conditions; (c) we apply clique-size bounding and design new enumeration order to approach the optimality conditions; and (d) to verify experimentally, we test eight real benchmark  ...  Maximal clique enumeration (MCE) is a fundamental problem in graph theory and is used in many applications, such as social network analysis, bioinformatics, intelligent agent systems, cyber security, etc  ...  We would like to thank Yujun Dai for her effort in the earlier version [44] .  ... 
arXiv:2009.10376v2 fatcat:qmmnt65uararbaw2jc6b4vjyga

Lightweight graphical models for selectivity estimation without independence assumptions

Kostas Tzoumas, Amol Deshpande, Christian S. Jensen
2011 Proceedings of the VLDB Endowment  
an interaction between Xi and Xj exists.  ...  For the second step, our propagation algorithm join indicator is in the worst case of the form (Ri .A, Rj .B, Jij ), proceeds as follows.  ... 
doi:10.14778/3402707.3402724 fatcat:7embbg4ya5errmtw43j7tx6s3q

Extremal and probabilistic results for regular graphs

Ewan Davies, Jozef Skokan, Peter Allen
We also cover applications to matchings and colourings, in each case proving a tight bound on an observable of a Gibbs distribution and deriving an extremal result on the number of a relevant combinatorial  ...  We then turn to a form of Szemerédi regularity in sparse hypergraphs, and develop a method for embedding complexes that generalises a widely-applied method for counting in pseudorandom graphs.  ...  Since the expectation is less than one, there must exist a colouring with zero monochromatic t-cliques.  ... 
doi:10.21953/lse.bijk2dsj3hlb fatcat:tlpyyan4wjbpfdibns3mft225e