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Randomly Rounding Rationals with Cardinality Constraints and Derandomizations
[chapter]

*
STACS 2007
*

We show how to generate randomized

doi:10.1007/978-3-540-70918-3_38
dblp:conf/stacs/Doerr07
fatcat:vgxd37eo7ncerhea2xqnrm4ieu
*roundings*of*rational*vectors that satisfy hard*cardinality**constraints**and*allow large deviations bounds. ... We call a*constraint*hard*constraint*if we require our solution to satisfy it without violation. In this paper, we are mainly concerned*with**cardinality**constraints*. ... General*Derandomization*In this section, we give a simple*derandomization*for the case that the*constraint*matrix A is*rational**and*we do not have hard*constraints*. ...##
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Randomized Rounding in the Presence of a Cardinality Constraint

2015
*
ACM Journal of Experimental Algorithmics
*

We regard the problem of generating randomized

doi:10.1145/2594409
fatcat:d6zlzyaglrfwzgwnwu3ad5ovc4
*roundings**with*a single*cardinality**constraint*. This is motivated by recent results of Srinivasan (FOCS 2001), Gandhi et al. ... Our experiments show that adding a single*cardinality**constraint*typically reduces the*rounding*errors*and*not seriously increases the running times. ... Most noteworthy is the*derandomization*of Srinivasan's randomized*roundings**with**cardinality**constraints*.*Derandomizing*Srinivasan's Randomized*Roundings*. ...##
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Randomized Rounding in the Presence of a Cardinality Constraint
[chapter]

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

We regard the problem of generating randomized

doi:10.1137/1.9781611972894.16
dblp:conf/alenex/DoerrW09
fatcat:jedu4qbxive73dkpm4cibag3mm
*roundings**with*a single*cardinality**constraint*. This is motivated by recent results of Srinivasan (FOCS 2001), Gandhi et al. ... Our experiments show that adding a single*cardinality**constraint*typically reduces the*rounding*errors*and*not seriously increases the running times. ... Most noteworthy is the*derandomization*of Srinivasan's randomized*roundings**with**cardinality**constraints*.*Derandomizing*Srinivasan's Randomized*Roundings*. ...##
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Linearly Representable Submodular Functions: An Algebraic Algorithm for Minimization

2020
*
International Colloquium on Automata, Languages and Programming
*

These problems are (i) covering a directed graph by k a-arborescences

doi:10.4230/lipics.icalp.2020.61
dblp:conf/icalp/GurjarR20
fatcat:o6tjumo5qfed7pp5xv7zvg7czm
*and*(ii) packing k branchings*with*given root sets in a directed graph. ... Further, we*derandomize*our algorithm so that it needs only O(log²(kn|E|)) many random bits. ... Given a*rational*point β ∈ R E , one needs to decide if β lies in P r ,*and*if not then find a violating*constraint*from the above set. ...##
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Distributed local approximation algorithms for maximum matching in graphs and hypergraphs
[article]

2020
*
arXiv
*
pre-print

*rounds*deterministically or Õ(log^3 n )

*rounds*

*randomly*. ... This gives an algorithm for (2 Δ - 1)-edge-list coloring in Õ(log^2 Δlog n)

*rounds*deterministically or Õ( (loglog n)^3 )

*rounds*

*randomly*. ... Next,

*randomly*choose an edge-coloring of H ′

*with*4∆ ′ r/δ colors,

*and*discard all pairs of adjacent edges

*with*the same color. ...

##
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Improved parallel approximation of a class of integer programming problems
[chapter]

1996
*
Lecture Notes in Computer Science
*

We present a method to

doi:10.1007/3-540-61440-0_159
fatcat:shqy2jxdkrgprkelpnanpxkmni
*derandomize*RN C algorithms, converting them to N C algorithms. ... This class includes problems such as global wire-routing in VLSI gate arrays*and*a generalization of telephone network planning in SONET rings. ... We thank Prabhakar Raghavan for clarifying an issue about randomized*rounding*,*and*David Zuckerman for pointing out the work of [8] . We also thank the referee for his/her helpful comments. ...##
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Improved parallel approximation of a class of integer programming problems

1997
*
Algorithmica
*

We present a method to

doi:10.1007/bf02523683
fatcat:7mmkyhnnbrbafldjieg5r55hxa
*derandomize*RN C algorithms, converting them to N C algorithms. ... This class includes problems such as global wire-routing in VLSI gate arrays*and*a generalization of telephone network planning in SONET rings. ... We thank Prabhakar Raghavan for clarifying an issue about randomized*rounding*,*and*David Zuckerman for pointing out the work of [8] . We also thank the referee for his/her helpful comments. ...##
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Component-by-component construction of low-discrepancy point sets of small size

2008
*
Monte Carlo Methods and Applications
*

To this end, we introduce the inverse of the star discrepancy of such a sequence,

doi:10.1515/mcma.2008.007
fatcat:fupdq45ravgfdh2oadyst7xybi
*and*derive upper bounds for it as well as for the star discrepancy of the projections of finite subsequences*with*explicitly ... This results in a deterministic algorithm that constructs N -point sets*with*small discrepancy in a component-by-component fashion. ... In order to be able to use existing*derandomizations*, we reformulate our problem of "adding one dimension" as a*rounding*problem*with*hard*constraints*. ...##
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Parallel Algorithms via the Probabilistic Method
[chapter]

2007
*
Handbook of Parallel Computing
*

We thank our students Sandro Esquivel

doi:10.1201/9781420011296.ch18
fatcat:hxzhixnhujcbxmrps62ks2pg7e
*and*Carsten Krapp for setting parts of the chapter in L A T E X. ... Last but not least we sincereley thank the editors for the invitation to contribute to the handbook, their patience*and*cooperation. ...*With*the method of limited independence we parallelize*and**derandomize*this*rounding*scheme in the next step. Step 4:*Derandomized**rounding*in N C. ...##
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Hardness of Solving Sparse Overdetermined Linear Systems

2009
*
ACM Transactions on Computation Theory
*

Formally, we prove that for every ε, δ > 0, given a system of linear equations

doi:10.1145/1595391.1595393
fatcat:xby4pxzqpra53adtfgmnwmf2vy
*with*integer coefficients where each equation is on 3 variables, it is NP-hard to distinguish between the following two cases ... A classic result due to Håstad established that for every constant ε > 0, given an overdetermined system of linear equations over a finite field Fq where each equation depends on exactly 3 variables*and*... Acknowledgments We thank Johan Håstad*and*the anonymous reviewers for very useful feedback which helped us improve the presentation of the paper. ...##
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Deterministic parallel algorithms for fooling polylogarithmic juntas and the Lovasz Local Lemma
[article]

2018
*
arXiv
*
pre-print

A series of papers, beginning

arXiv:1610.03383v10
fatcat:44oepp3pubeefo4zrjf7fh73km
*with*Luby (1993)*and*continuing*with*Berger & Rompel (1991)*and*Chari et al. (2000), showed that these techniques can be combined to give deterministic parallel algorithms ... Many randomized algorithms can be*derandomized*efficiently using either the method of conditional expectations or probability spaces*with*low (almost-) independence. ... Let p ∈ [0, 1] n be a vector of probabilities, wherein each entry p i is a*rational*number*with*denominator 2 b . ...##
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Fault-Tolerant Facility Location: A Randomized Dependent LP-Rounding Algorithm
[chapter]

2010
*
Lecture Notes in Computer Science
*

We extend this approach

doi:10.1007/978-3-642-13036-6_19
fatcat:zxbh76qkfjevjno4npvs3mo3r4
*and*construct a laminar family of clusters, which then guides the*rounding*procedure. ... It allows to exploit properties of dependent*rounding*,*and*provides a quite tight analysis resulting in the improved approximation ratio. ... Let ⊆ [ ] be any subset*with**cardinality*≥ 2,*and*let = ( 0 , 1 , 2 , . . . , ) be any vector, such that for all*with*0 ≤ ≤ −2 we have −2 +1 + +2 ≤ 0. Then, E[ , (ˆ)] ≥ E[ , (ℛ( ))]. Theorem 2. ...##
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Polynomial-Time Approximation Schemes
[chapter]

2007
*
Handbook of Approximation Algorithms and Metaheuristics
*

This type of approximation algorithm is called a dual approximation algorithm [23] or approximation

doi:10.1201/9781420010749.ch9
fatcat:ixamu4bulfgkjjzfu3cfj5i6se
*with*resource augmentation [8] . ... 2 Definition 1.2 A randomized approximation scheme for an optimization problem Π is an algorithm A which takes as input both the instance I*and*an error bound ε, runs in time polynomial in |I|*and*has ... [9] for the knapsack problem*with**cardinalities**constraints*. ...##
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Approximation Algorithms for NP-Hard Problems

2004
*
Oberwolfach Reports
*

Combinatorial Auctions Without Randomized

doi:10.4171/owr/2004/28
fatcat:fwbs36pgpjev5gk6cfeb7ylukm
*Rounding*. 2 Oberwolfach Report 28/2004 The meeting was held in very informal*and*stimulating atmosphere. ... The workshop was concerned*with*the most important recent developments in the area of efficient approximation algorithms for NP-hard optimization problems as well as*with*new techniques for proving intrinsic ... If there exists a feasible*rounding*then this*rounded*solution is a 2-approximation. For |d| > 1 the inverse transformation yields*rationals**with*denominator 2d at most. ...##
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Approximability of average completion time scheduling on unrelated machines

2016
*
Mathematical programming
*

The improvement is made by modifying

doi:10.1007/s10107-016-1004-8
fatcat:6u5cw6zic5awlfaaomymfwwiwy
*and*combining known algorithms*and*by the use of new lower bounds. These results improve on the known N P-hardness*and*2-approximability. ... This provides one of the last missing pieces in the complexity classification of machine scheduling*with*(weighted) sum of completion times objective. ... reproduction in any medium, provided you give appropriate credit to the original author(s)*and*the source, provide a link to the Creative Commons license,*and*indicate if changes were made. ...
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