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Derandomized Squaring of Graphs
[chapter]

2005
*
Lecture Notes in Computer Science
*

We introduce a "

doi:10.1007/11538462_37
fatcat:wpjiq4l2qnamvhwk57wi2phrna
*derandomized*" analogue*of**graph**squaring*. ... This operation increases the connectivity*of*the*graph*(as measured by the second eigenvalue) almost as well as*squaring*the*graph*does, yet only increases the degree*of*the*graph*by a constant factor, ... Acknowledgments This work emerged from*of*our collaborations with Omer Reingold, Luca Trevisan, and Avi Wigderson. We are deeply grateful to them for their insights on this topic ...##
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Deterministic Approximation of Random Walks in Small Space

2019
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

Second, we define and analyze a generalization

doi:10.4230/lipics.approx-random.2019.42
dblp:conf/approx/MurtaghRSV19
fatcat:qbobogy745ds7b43u23fx3oj4y
*of*the*derandomized**square*for irregular*graphs*and for sparsifying the product*of*two distinct*graphs*. ... Our algorithm combines the*derandomized**square**graph*operation [21] , which we recently used for solving Laplacian systems in nearly logarithmic space [16] , with ideas from [5] , which gave an algorithm ... Our solution is to generalize the*derandomized**square*to produce sparse approximations to the product*of*distinct*graphs*. ...##
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Deterministic Approximation of Random Walks in Small Space
[article]

2019
*
arXiv
*
pre-print

Second, we define and analyze a generalization

arXiv:1903.06361v2
fatcat:6mm4uijvojg5fggde4zqsmemxa
*of*the*derandomized**square*for irregular*graphs*and for sparsifying the product*of*two distinct*graphs*. ... Our algorithm combines the*derandomized**square**graph*operation (Rozenman and Vadhan, 2005), which we recently used for solving Laplacian systems in nearly logarithmic space (Murtagh, Reingold, Sidford, ... Our solution is to generalize the*derandomized**square*to produce sparse approximations to the product*of*distinct*graphs*. ...##
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Derandomization Beyond Connectivity: Undirected Laplacian Systems in Nearly Logarithmic Space

2017
*
2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
*

We give a deterministicÕ(log n)-space algorithm for approximately solving linear systems given by Laplacians

doi:10.1109/focs.2017.79
dblp:conf/focs/MurtaghRSV17
fatcat:hw3sxqd5wvgnljea3yrdqb54oy
*of*undirected*graphs*, and consequently also approximating hitting times, commute times, and ... escape probabilities for undirected*graphs*. ... We obtain a sequence*of**graphs*G 0 , G 1 , . . . , G k , where G 0 = G and G i is the*derandomized**square**of*G i−1 , a*graph**of*degree d · c i . ...##
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Derandomization Beyond Connectivity: Undirected Laplacian Systems in Nearly Logarithmic Space
[article]

2017
*
arXiv
*
pre-print

We give a deterministic Õ( n)-space algorithm for approximately solving linear systems given by Laplacians

arXiv:1708.04634v1
fatcat:mooju4ooy5ezlpnhajkoyghcy4
*of*undirected*graphs*, and consequently also approximating hitting times, commute times, and escape ... probabilities for undirected*graphs*. ...*Derandomized**squaring**of**graphs*. ...##
###
An Optimal Lower Bound for Monotonicity Testing over Hypergrids
[chapter]

2013
*
Lecture Notes in Computer Science
*

Approximating Chromatic Number
Sangxia Huang
12:14-1:45 Lunch
1:45-3:13 RANDOM (Random structures)
3:13-3:30 Break
3:30-4:36 APPROX
Online

doi:10.1007/978-3-642-40328-6_30
fatcat:tdimjhbxkveu5l724kwo37lina
*Square*-into-*Square*Packing Sandor Fekete and Hella-Franziska ... Problems on Planar*Graphs*Feng Pan and Aaron Schild Approximation Algorithms for Movement Repairmen Mohammadtaghi Hajiaghayi, Rohit Khandekar, Reza Khani and Guy Kortsarz The Approximability*of*the Binary ...##
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Derandomized graph products

1995
*
Computational Complexity
*

We show that this reduction can be made deterministic (

doi:10.1007/bf01277956
fatcat:xjuibrzzv5eznh5braolfndyki
*derandomized*), using random walks on expander*graphs*[1]. ... The main technical contribution*of*this paper is in lower bounding the probability that all steps*of*a random walk stay within a specified set*of*vertices*of*a*graph*. ... Since our technique is a*derandomization**of*the Berman and Schnitger technique, we call it*derandomized**graph*products. ...##
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Small-Bias Sets for Nonabelian Groups: Derandomizing the Alon-Roichman Theorem
[article]

2013
*
arXiv
*
pre-print

Our techniques include

arXiv:1304.5010v4
fatcat:mv5pjrun5jfv7hyrqhmcytje4m
*derandomized**squaring*(in both the matrix product and tensor product senses) and a Chernoff-like bound on the expected norm*of*the product*of*independently random operators that ... Equivalently, such sets make G's Cayley*graph*an expander with eigenvalue |lambda| <= epsilon. The Alon-Roichman theorem shows that random sets*of*size O(log |G| / epsilon^2) suffice. ...*derandomized**squaring*. ...##
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High-precision Estimation of Random Walks in Small Space

2020
*
2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
*

A running theme throughout these contributions is an analysis

doi:10.1109/focs46700.2020.00123
fatcat:oydcdvq7cjg4leezgeeljnldce
*of*"cycle-lifted*graphs*," where we take a*graph*and "lift" it to a new*graph*whose adjacency matrix is the tensor product*of*the original adjacency ... We also give improvements on the space complexity*of*both*of*these previous algorithms for non-Eulerian directed*graphs*when the error is negligible (ǫ = 1/N ω(1) ), generalizing what Hoza and Zuckerman ... Acknowledgements We thank William Hoza for pointing out an error in an earlier version*of*Theorem 4.8. ...##
###
High-precision Estimation of Random Walks in Small Space
[article]

2022
*
arXiv
*
pre-print

A running theme throughout these contributions is an analysis

arXiv:1912.04524v3
fatcat:peiozxcjrff75c53cvzlx2daju
*of*"cycle-lifted*graphs*", where we take a*graph*and "lift" it to a new*graph*whose adjacency matrix is the tensor product*of*the original adjacency ... We also give improvements on the space complexity*of*both*of*these previous algorithms for non-Eulerian directed*graphs*when the error is negligible (ϵ=1/N^ω(1)), generalizing what Hoza and Zuckerman ( ... We thank William Hoza for pointing out an error in an earlier version*of*Theorem 4.8 and Ori Sberlo and Dean Doron for finding a bug in an earlier version*of*the proof*of*Theorem 5.9. ...##
###
Derandomization of Euclidean Random Walks
[chapter]

2007
*
Lecture Notes in Computer Science
*

We consider the problem

doi:10.1007/978-3-540-74208-1_26
fatcat:p56crfbuf5dblkxsguavymlpzy
*of**derandomizing*random walks in the Euclidean space R k . ... As a corollary, we show that the Dirichlet Problem can be deterministically simulated in space O(log n √ log log n), where 1/n is the desired precision*of*the simulation. ... Attempts to solve DirDP, which is at least as hard as*derandomizing*the class BPSPACE(S), can now be restricted to different classes*of**graphs*. ...##
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Spectral Sparsification via Bounded-Independence Sampling

2020
*
International Colloquium on Automata, Languages and Programming
*

We give a deterministic, nearly logarithmic-space algorithm for mild spectral sparsification

doi:10.4230/lipics.icalp.2020.39
dblp:conf/icalp/DoronMVZ20
fatcat:i4wyqtosjzhqlpihlef3djthdm
*of*undirected*graphs*. ... Given a weighted, undirected*graph*G on n vertices described by a binary string*of*length N, an integer k ≤ log n and an error parameter ε > 0, our algorithm runs in space Õ(k log(N w_max/w_min)) where ... 2 in G. 39:4 Spectral Sparsification via Bounded-Independence Sampling and Vadhan [41] showed that the*derandomized**square*actually produces a spectral sparsifier*of*the*square**of*a*graph*and this ...##
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Pseudorandom Bit Generators That Fool Modular Sums
[chapter]

2009
*
Lecture Notes in Computer Science
*

The most interesting technical component

doi:10.1007/978-3-642-03685-9_46
fatcat:xafdsn5p2fcadib7fd7ayrd2ey
*of*our second construction is a variant*of*the*derandomized**graph**squaring*operation*of*[RV]. ... Our generalization handles a product*of*two distinct*graphs*with distinct bounds on their expansion. ... Here we study the analogue*of**derandomized**squaring*for taking products*of*two distinct Cayley*graphs*over an abelian group (namely Z M ). ...##
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Randomized Rounding in the Presence of a Cardinality Constraint

2015
*
ACM Journal of Experimental Algorithmics
*

Our work results in (a) an improved version

doi:10.1145/2594409
fatcat:d6zlzyaglrfwzgwnwu3ad5ovc4
*of*the bitwise*derandomization*given by the first author, (b) the first*derandomization**of*Srinivasan's treebased randomized approach, together with a proof ... When implementing the*derandomized*tree-based approach, however, the choice*of*the tree is important. ... Our first set*of*tests are*square*random matrices with 0/1 entries. ...##
###
Randomized Rounding in the Presence of a Cardinality Constraint
[chapter]

2009
*
2009 Proceedings of the Eleventh Workshop on Algorithm Engineering and Experiments (ALENEX)
*

Our work results in (a) an improved version

doi:10.1137/1.9781611972894.16
dblp:conf/alenex/DoerrW09
fatcat:jedu4qbxive73dkpm4cibag3mm
*of*the bitwise*derandomization*given by the first author, (b) the first*derandomization**of*Srinivasan's treebased randomized approach, together with a proof ... When implementing the*derandomized*tree-based approach, however, the choice*of*the tree is important. ... Our first set*of*tests are*square*random matrices with 0/1 entries. ...
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