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Randomly Rounding Rationals with Cardinality Constraints and Derandomizations [chapter]

Benjamin Doerr
STACS 2007  
We show how to generate randomized 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.  ... 
doi:10.1007/978-3-540-70918-3_38 dblp:conf/stacs/Doerr07 fatcat:vgxd37eo7ncerhea2xqnrm4ieu

Randomized Rounding in the Presence of a Cardinality Constraint

Benjamin Doerr, Magnus Wahlström
2015 ACM Journal of Experimental Algorithmics  
We regard the problem of generating randomized 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.  ... 
doi:10.1145/2594409 fatcat:d6zlzyaglrfwzgwnwu3ad5ovc4

Randomized Rounding in the Presence of a Cardinality Constraint [chapter]

Benjamin Doerr, Magnus Wahlström
2009 2009 Proceedings of the Eleventh Workshop on Algorithm Engineering and Experiments (ALENEX)  
We regard the problem of generating randomized 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.  ... 
doi:10.1137/1.9781611972894.16 dblp:conf/alenex/DoerrW09 fatcat:jedu4qbxive73dkpm4cibag3mm

Linearly Representable Submodular Functions: An Algebraic Algorithm for Minimization

Rohit Gurjar, Rajat Rathi, Emanuela Merelli, Anuj Dawar, Artur Czumaj
2020 International Colloquium on Automata, Languages and Programming  
These problems are (i) covering a directed graph by k a-arborescences 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.  ... 
doi:10.4230/lipics.icalp.2020.61 dblp:conf/icalp/GurjarR20 fatcat:o6tjumo5qfed7pp5xv7zvg7czm

Distributed local approximation algorithms for maximum matching in graphs and hypergraphs [article]

David G. Harris
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.  ... 
arXiv:1807.07645v7 fatcat:4yaui54cd5ahhhac7byids5k6u

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

Noga Alon, Aravind Srinivasan
1996 Lecture Notes in Computer Science  
We present a method to 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.  ... 
doi:10.1007/3-540-61440-0_159 fatcat:shqy2jxdkrgprkelpnanpxkmni

Improved parallel approximation of a class of integer programming problems

N. Alon, A. Srinivasan
1997 Algorithmica  
We present a method to 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.  ... 
doi:10.1007/bf02523683 fatcat:7mmkyhnnbrbafldjieg5r55hxa

Component-by-component construction of low-discrepancy point sets of small size

Benjamin Doerr, Michael Gnewuch, Peter Kritzer, Friedrich Pillichshammer
2008 Monte Carlo Methods and Applications  
To this end, we introduce the inverse of the star discrepancy of such a sequence, 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.  ... 
doi:10.1515/mcma.2008.007 fatcat:fupdq45ravgfdh2oadyst7xybi

Parallel Algorithms via the Probabilistic Method [chapter]

Anand Srivastav, Lasse Kliemann
2007 Handbook of Parallel Computing  
We thank our students Sandro Esquivel 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.  ... 
doi:10.1201/9781420011296.ch18 fatcat:hxzhixnhujcbxmrps62ks2pg7e

Hardness of Solving Sparse Overdetermined Linear Systems

Venkatesan Guruswami, Prasad Raghavendra
2009 ACM Transactions on Computation Theory  
Formally, we prove that for every ε, δ > 0, given a system of linear equations 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.  ... 
doi:10.1145/1595391.1595393 fatcat:xby4pxzqpra53adtfgmnwmf2vy

Deterministic parallel algorithms for fooling polylogarithmic juntas and the Lovasz Local Lemma [article]

David G. Harris
2018 arXiv   pre-print
A series of papers, beginning 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 .  ... 
arXiv:1610.03383v10 fatcat:44oepp3pubeefo4zrjf7fh73km

Fault-Tolerant Facility Location: A Randomized Dependent LP-Rounding Algorithm [chapter]

Jaroslaw Byrka, Aravind Srinivasan, Chaitanya Swamy
2010 Lecture Notes in Computer Science  
We extend this approach 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.  ... 
doi:10.1007/978-3-642-13036-6_19 fatcat:zxbh76qkfjevjno4npvs3mo3r4

Polynomial-Time Approximation Schemes [chapter]

Hadas Shachnai, Tami Tamir
2007 Handbook of Approximation Algorithms and Metaheuristics  
This type of approximation algorithm is called a dual approximation algorithm [23] or approximation 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.  ... 
doi:10.1201/9781420010749.ch9 fatcat:ixamu4bulfgkjjzfu3cfj5i6se

Approximation Algorithms for NP-Hard Problems

Ravindran Kannan, Marek Karpinski
2004 Oberwolfach Reports  
Combinatorial Auctions Without Randomized 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.  ... 
doi:10.4171/owr/2004/28 fatcat:fwbs36pgpjev5gk6cfeb7ylukm

Approximability of average completion time scheduling on unrelated machines

René Sitters
2016 Mathematical programming  
The improvement is made by modifying 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.  ... 
doi:10.1007/s10107-016-1004-8 fatcat:6u5cw6zic5awlfaaomymfwwiwy
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