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Computing large independent sets in a single round

Magnús M. Halldórsson, Christian Konrad
2017 Distributed computing  
A classic result of Linial shows that a constant number of rounds does not suffice to compute a maximal independent set.  ...  Independent sets play a central role in distributed algorithmics. We examine here the minimal requirements for computing non-trivial independent sets.  ...  Acknowledgements We are grateful for the comments of an anonymous reviewer, which resulted in a sharpened focus of the paper.  ... 
doi:10.1007/s00446-017-0298-y fatcat:7tlxh7u7xndlxm75knoc6i7vda

Distributed Large Independent Sets in One Round on Bounded-Independence Graphs [chapter]

Magnús M. Halldórsson, Christian Konrad
2015 Lecture Notes in Computer Science  
We present a randomized one-round, single-bit messages, distributed algorithm for the maximum independent set problem in polynomially bounded-independence graphs with poly-logarithmic approximation factor  ...  Then, for O(1)-claw free graphs (which include graphs of bounded-independence), we show that using a different algorithm, an independent set of expected size Θ(β(G)) can be computed in one round using  ...  Distributed Large Independent Sets in One Round On Bounded-independence Graphs Magnús M. Halldórsson Abstract.  ... 
doi:10.1007/978-3-662-48653-5_37 fatcat:aajtwbw3bbfangz76xvuj67glu

Round compression for parallel matching algorithms

Artur Czumaj, Jakub Łącki, Aleksander Mądry, Slobodan Mitrović, Krzysztof Onak, Piotr Sankowski
2018 Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2018  
It is well known that in the PRAM model one can compute a 2-approximate maximum matching in O(log n) rounds.  ...  (SPAA 2011) showed that if each machine has n 1+Ω(1) memory, this problem can also be solved 2-approximately in a constant number of rounds.  ...  We start by showing that EmulatePhase computes a large matching as follows.  ... 
doi:10.1145/3188745.3188764 dblp:conf/stoc/CzumajLMMOS18 fatcat:h5545lg36nd63fpbcluxfuflf4

Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space [article]

Artur Czumaj, Peter Davies, Merav Parter
2020 arXiv   pre-print
Matching and Maximal Independent Set.  ...  A major challenge underlying the sublinear space setting is that the local space of each machine might be too small to store all the edges incident to a single node.  ...  We need to have 2-hop neighborhoods stored on a single machine in order for it to determine which edges/nodes are in the matching or independent set.  ... 
arXiv:1912.05390v3 fatcat:oj2d5kzlhndebhd2ydvwx2q6la

Non-independent Randomized Rounding and an Application to Digital Halftoning [chapter]

Benjamin Doerr, Henning Schnieder
2002 Lecture Notes in Computer Science  
Instead of independently rounding the variables (expected error 0.82944 per box in the worst case), we impose a number of suitable dependencies.  ...  We present a randomized algorithm computing roundings with expected error at most 0.6287 per box, improving the 0.75 non-constructive bound of Asano et al.  ...  Acknowledgments We would like to thank Tetsuo Asano, Naoki Katoh, Koji Obokata and Takeshi Tokuyama for providing us with a preprint of their SODA 2002 paper and some useful discussion on the topic.  ... 
doi:10.1007/3-540-45749-6_37 fatcat:ffhfd6r5tvdnbdvxq6nyhw76ey

Nonindependent Randomized Rounding and an Application to Digital Halftoning

Benjamin Doerr
2005 SIAM journal on computing (Print)  
Instead of independently rounding the variables (expected error 0.82944 per box in the worst case), we impose a number of suitable dependencies.  ...  We present a randomized algorithm computing roundings with expected error at most 0.6287 per box, improving the 0.75 non-constructive bound of Asano et al.  ...  Acknowledgments We would like to thank Tetsuo Asano, Naoki Katoh, Koji Obokata and Takeshi Tokuyama for providing us with a preprint of their SODA 2002 paper and some useful discussion on the topic.  ... 
doi:10.1137/s0097539703430154 fatcat:bhoy7nuxmveptlaqehh6adufgu

Efficient Large-Scale Multiple Migration Planning and Scheduling in SDN-enabled Edge Computing [article]

TianZhang He, Adel N Toosi, Rajkumar Buyya
2021 arXiv   pre-print
We propose an iterative Maximal Independent Set (MIS)-based multiple migration planning and scheduling algorithm.  ...  scenarios in edge computing.  ...  Since, we have a contradiction, it must be that I q is a maximal independent set. Single-Round MCs Algorithm Furthermore, we propose a single-round MCs-based algorithm (single-MCs).  ... 
arXiv:2111.08936v1 fatcat:oz2pwpnbxvgjxbjgbjm2bl53s4

Exploring the Resilience of Some Lightweight Ciphers Against Profiled Single Trace Attacks [chapter]

Valentina Banciu, Elisabeth Oswald, Carolyn Whitnall
2015 Lecture Notes in Computer Science  
In particular, the more (reasonably statistically independent) intermediate values are produced in a target implementation, the better attacks succeed.  ...  We show that mainly the diffusion properties of both the round function and the key schedule play a role.  ...  Whitnall have been supported in part by EPSRC via grant EP/I005226/1. The authors would like to thank the anonymous reviewers for the useful comments and suggestions.  ... 
doi:10.1007/978-3-319-21476-4_4 fatcat:cdvxezxshnh5hnmyhm6wi27qg4

Multivariate Profiling of Hulls for Linear Cryptanalysis

Andrey Bogdanov, Elmar Tischhauser, Philip S. Vejre
2018 IACR Transactions on Symmetric Cryptology  
In this paper, we develop a model for linear cryptanalysis using multiple linearly independent approximations which takes key-dependence into account and complies with Nyberg's result.  ...  multivariate distribution of the signal correlations for a large number of keys, thereby entirely avoiding assumptions regarding the shape of this distribution.  ...  By computing Equation 4 for a large number of keys, we obtain a set of values drawn from D α,β .  ... 
doi:10.46586/tosc.v2018.i1.101-125 fatcat:i2a2jqaonfa6xjffkfksk3im5q

Parallel computation on interval graphs using PC clusters: Algorithms and experiments [chapter]

A. Ferreira, I. Guérin Lassous, K. Marcus, A. Rau-Chaplin
1998 Lecture Notes in Computer Science  
interval covering, maximum independent set and minimum dominating set.  ...  The use of PC clusters interconnected by high performance local networks is one of the major current trends in parallel/distributed computing.  ...  The maximum independent set and the minimum dominating set problems in interval graphs can be solved using a CaM(n, p) in O ( rs( ~, p)+logp) time, with O(logp) communication rounds.  ... 
doi:10.1007/bfb0057943 fatcat:2lltogfmgrelfpyvmlw22r2yhy

Breaking the Linear-Memory Barrier in MPC: Fast MIS on Trees with Strongly Sublinear Memory [article]

Sebastian Brandt and Manuela Fischer and Jara Uitto
2019 arXiv   pre-print
In particular, we show that the Maximal Independent Set (MIS) problem can be solved efficiently, that is, in O(log^3 log n) rounds, when the input graph is a tree.  ...  In contrast to the linear-memory MPC model and also to streaming algorithms, in this low-memory MPC setting, a single machine will only see a small number of nodes in the graph.  ...  There is an O(log ∆)-round LOCAL algorithm that computes an independent set on an n-node graph with maximum degree ∆ so that the remainder graph, after removal of all nodes in the independent set and their  ... 
arXiv:1802.06748v3 fatcat:njedklaufrgndnz6nv4hubhmda

Deterministic Massively Parallel Algorithms for Ruling Sets [article]

Shreyas Pai, Sriram V. Pemmaraju
2022 arXiv   pre-print
In this paper we present a deterministic O(loglog n)-round algorithm for the 2-ruling set problem in the Massively Parallel Computation model with Õ(n) memory; this algorithm also runs in O(loglog n) rounds  ...  This is exponentially faster than the fastest known deterministic 2-ruling set algorithm for these models, which is simply the O(logΔ)-round deterministic Maximal Independent Set algorithm due to Czumaj  ...  Acknowledgement: We thank the anonymous reviewer who suggested a simplification to our approach that also led to an improvement in the running time of Algorithm 1.  ... 
arXiv:2205.12686v1 fatcat:muurzvg3tzfvbocmyot4qst3sm

A Single-Key Attack on the Full GOST Block Cipher

Takanori Isobe
2012 Journal of Cryptology  
The Point of the attack : Find independent sets of master key bit such as A1 and A2 We need to construct large set of independent keys.  ...  set of keys that transforms P to X for 4-round unit" Equivalent Keys 4 round P k 1 ||…||k 4 K1 X Categorize K1 into sets of equivalent keys depending on values of X K1 Fix 2 64 a set  ... 
doi:10.1007/s00145-012-9118-5 fatcat:bgipiekbn5fsvhfw233oz5pjsu

Multivariate Profiling of Hulls for Linear Cryptanalysis

Andrey Bogdanov, Elmar Tischhauser, Philip S. Vejre
2018 IACR Transactions on Symmetric Cryptology  
In this paper, we develop a model for linear cryptanalysis using multiple linearly independent approximations which takes key-dependence into account and complies with Nyberg's result.  ...  multivariate distribution of the signal correlations for a large number of keys, thereby entirely avoiding assumptions regarding the shape of this distribution.  ...  By computing Equation 4 for a large number of keys, we obtain a set of values drawn from D α,β .  ... 
doi:10.13154/tosc.v2018.i1.101-125 dblp:journals/tosc/BogdanovTV18 fatcat:22fdcgq5sfeihn2izp3esoq5ei

DFEP: Distributed Funding-Based Edge Partitioning [chapter]

Alessio Guerrieri, Alberto Montresor
2015 Lecture Notes in Computer Science  
Each partition starts from a random edge and expands independently by spending currency to buy neighboring edges.  ...  An alternative approach divides the edge set, with the goal of obtaining more balanced partitions in presence of high-degree nodes, such as hubs in real world networks, that can be split between distinct  ...  Both versions of PowerGraph work in a single pass over the edge set, and therefore is a better choice if the amount of computation needed after the partitioning step is not large enough to warrant a more  ... 
doi:10.1007/978-3-662-48096-0_27 fatcat:qmcelraajvdrzeg5qda663fjdy
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