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On Complexity of 1-Center in Various Metrics [article]

Amir Abboud, MohammadHossein Bateni, Vincent Cohen-Addad, Karthik C. S., Saeed Seddighin
2021 arXiv   pre-print
Moreover, we extend one of our hardness results to rule out subquartic algorithms for the well-studied 1-median problem in the edit metric, where given a set of n strings each of length n, the goal is  ...  On the other hand, assuming the hitting set conjecture (HSC), we show that when d=ω(log n), no subquadratic algorithm can solve 1-center problem in any of the ℓ_p-metrics, or in edit or Ulam metrics. ∙  ...  Klein, editor, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algo- rithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 2012–  ... 
arXiv:2112.03222v1 fatcat:qlknjrjlqzdtdely3eq45cvsmu

Optimal Vertex Fault Tolerant Spanners (for fixed stretch) [chapter]

Greg Bodwin, Michael Dinitz, Merav Parter, Virginia Vassilevska Williams
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
It is easy to verify that this algorithm never creates cycles of length 2k  ...  In fact, their existentially optimal upper bound was obtained via an extremely simple and natural greedy construction algorithm: consider the edges of G in non-decreasing order of their weight and add  ...  In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 1479-1496, 2017.  ... 
doi:10.1137/1.9781611975031.123 dblp:conf/soda/BodwinDPW18 fatcat:t5sr4ib7freujfdjufj4sidzqe

Static pricing for multi-unit prophet inequalities [article]

Shuchi Chawla, Nikhil Devanur, Thodoris Lykouris
2021 arXiv   pre-print
On the other end of the spectrum, as k goes to infinity, the asymptotic performance of both static and adaptive pricing is well understood.  ...  Astonishingly, for k<20, it even outperforms the state-of-the-art adaptive pricing for the small-k regime.  ...  In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 1671–1687, 2017. 4  ... 
arXiv:2007.07990v2 fatcat:ka37h7wrjjhktjshkfdse5regy

Faster Maxflow via Improved Dynamic Spectral Vertex Sparsifiers [article]

Jan van den Brand, Yu Gao, Arun Jambulapati, Yin Tat Lee, Yang P. Liu, Richard Peng, Aaron Sidford
2021 arXiv   pre-print
Our algorithm implies a O(m^3/2-1/58log U) time maxflow algorithm, improving over the O(m^3/2-1/328log U) time maxflow algorithm of [Gao-Liu-Peng FOCS 2021].  ...  A procedure for turning algorithms for estimating a sequence of vectors under updates from an oblivious adversary to one that tolerates adaptive adversaries via the Gaussian-mechanism from differential  ...  shortest paths and unit capacity minimum cost flow in O(m In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta  ... 
arXiv:2112.00722v1 fatcat:v5fv24yzpbdrzlkeso4ofz5haq

A constant-time algorithm for middle levels Gray codes [article]

Torsten Mütze, Jerri Nummenpalo
2019 arXiv   pre-print
To appear in ACM Transactions on Algorithms, 2018] this existence proof was turned into an algorithm that computes each new set in the Gray code in time O(n) on average.  ...  In this work we present an algorithm for computing a middle levels Gray code in optimal time and space: each new set is generated in time O(1) on average, and the required space is O(n).  ...  In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 2238–2253, 2017.  ... 
arXiv:1606.06172v6 fatcat:25lf3f2sfzgzrox2uwfhpimeem

Maximizing Determinants under Matroid Constraints [article]

Vivek Madan, Aleksandar Nikolov, Mohit Singh, Uthaipon Tantipongpipat
2020 arXiv   pre-print
Our main result is a new approximation algorithm with an approximation guarantee that depends only on the dimension d of the vectors and not on the size k of the output set.  ...  Finally, we use the estimation algorithm and sparsity results to give an efficient deterministic approximation algorithm with an approximation guarantee that depends solely on the dimension d.  ...  Klein, editor, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 130-142. SIAM, 2017.  ... 
arXiv:2004.07886v1 fatcat:2z4i3t4wujggvpwd4lst7m6uf4

A Subquadratic Approximation Scheme for Partition [article]

Marcin Mucha, Karol Węgrzycki, Michał Włodarczyk
2018 arXiv   pre-print
To the best of our knowledge, this is the first NP-hard problem that has been shown to admit a subquadratic time approximation scheme, i.e., one with time complexity of O((n+1/ε)^2-δ) for some δ>0.  ...  The subject of this paper is the time complexity of approximating Knapsack, Subset Sum, Partition, and some other related problems.  ...  Klein, editor, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 2215-2229. SIAM, 2017.  ... 
arXiv:1804.02269v1 fatcat:4oapl5qvxzbcro2ylgkmixzm4u

A population protocol for exact majority with O(^5/3 n) stabilization time and asymptotically optimal number of states [article]

Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Dominik Kaaser, Peter Kling, Tomasz Radzik
2018 arXiv   pre-print
The standard design framework for majority protocols is based on O( n) phases and requires that all nodes are well synchronized within each phase, leading naturally to upper bounds of the order of at least  ...  [SODA 2018] showed that any exact-majority protocol which stabilizes in expected O(n^1-ϵ) parallel time, for any constant ϵ > 0, requires Ω( n) states.  ...  In 53rd Annual IEEE Symposium on Foundations of Com- Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 2560-2579.  ... 
arXiv:1805.05157v2 fatcat:e6xzqaj2hjaa7bsdajrqcrm2be

Bi-Arc Digraphs and Conservative Polymorphisms [article]

Pavol Hell and Akbar Rafiey and Arash Rafiey
2020 arXiv   pre-print
On the one hand, they are precisely the digraphs that admit certain polymorphisms of interest in the study of constraint satisfaction problems; on the other hand, they are a very broad generalization of  ...  There is much interest in understanding structures that admit particular types of polymorphisms, and especially in their recognition algorithms. (Such problems are referred to as metaproblems.)  ...  In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on 54 Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January  ... 
arXiv:1608.03368v5 fatcat:es537slt4fgz5d6ke25aqcdjby

An Asymptotically Optimal Algorithm for Maximum Matching in Dynamic Streams

Sepehr Assadi, Vihan Shah, Mark Braverman
2022
A long line of work on the dynamic streaming matching problem has reduced the gap between space upper and lower bounds first to n^{o(1)} factors [Assadi-Khanna-Li-Yaroslavtsev; SODA 2016] and subsequently  ...  instances to focus on.  ...  Acknowledgements We thank the anonymous reviewers of ITCS 2022 for their many insightful suggestions that helped with improving the presentation of this paper.  ... 
doi:10.4230/lipics.itcs.2022.9 fatcat:3rc3sjhtvvahhmtxlx4ch6a55m

Submodular Dominance and Applications

Frederick Qiu, Sahil Singla, Amit Chakrabarti, Chaitanya Swamy
2022
In submodular optimization we often deal with the expected value of a submodular function f on a distribution 𝒟 over sets of elements.  ...  We observe that WNR distributions satisfy Submodular Dominance, whereby the expected value of f under 𝒟 is at least the expected value of f under a product distribution with the same element-marginals  ...  In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 1671-1687, 2017. 36 Alexander Schrijver.  ... 
doi:10.4230/lipics.approx/random.2022.44 fatcat:cz3yp32ukfecdl4urswajectpu

st Symposium on Simplicity in Algorithms New Orleans LA, USA Co-located with The 29th ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)

Raimund Seidel
2018 unpublished
In an earlier version of the proof of Theorem 3, we erroneously claimed that, conditioned on the current sampling rate being 1/2 j , edges in E t α had been sampled at that rate.  ...  Ravi and Madhur Tulsiani for helpful discussions and comments on the presentation. Acknowledgement.  ...  Klein, editor, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 2190- 2202.  ... 
fatcat:tvuaojfsvjgfjaj7en2x4wdbhy