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Near approximation of maximum weight matching through efficient weight reduction
[article]

2011
*
arXiv
*
pre-print

We show that if we can approximate

arXiv:1012.5911v2
fatcat:ybhxs7q5vvcy5kqde42geeszwe
*a**maximum**weight*matching in G within factor alpha in time T(n,m,W) then we can find*a*matching*of**weight*at least (alpha-epsilon) times the*maximum**weight**of**a*matching ... In particular, if we combine our result with the recent (1-\epsilon)-approximation*algorithm*for*maximum**weight*matching in graphs due to Duan*and*Pettie whose time complexity has*a*poly-logarithmic dependence ... Acknowledgments The authors are very grateful to Seth Pettie for his valuable suggestions to apply the second (1 − ǫ)-approximation*algorithm*from [7] instead*of*the first one*and*to eliminate an n log ...##
###
Boosting Data Reduction for the Maximum Weight Independent Set Problem Using Increasing Transformations
[article]

2020
*
arXiv
*
pre-print

Given

arXiv:2008.05180v2
fatcat:il2uanigjrgj5p6nqkvtuuvtje
*a*vertex-*weighted*graph, the*maximum**weight**independent**set*problem asks for*a*pair-wise non-adjacent*set**of*vertices such that the sum*of*their*weights*is*maximum*. ... We introduce new generalized data*reduction**and*transformation rules for the problem.*A*key feature*of*our work is that some transformation rules can increase the size*of*the input. ... Let I be*a**maximum**weight**independent**set*in G*and*α w (G ) its*weight*. ...##
###
Near Approximation of Maximum Weight Matching through Efficient Weight Reduction
[chapter]

2011
*
Lecture Notes in Computer Science
*

We show that if we can approximate

doi:10.1007/978-3-642-20877-5_6
fatcat:jd5e7wdhkbhwldraw5furxxeli
*a**maximum**weight*matching in G within factor α in time T (n, m, W ) then we can find*a*matching*of**weight*at least (α − ǫ) times the*maximum**weight**of**a*matching in G ... in time In particular, if we combine our result with the recent (1 − ǫ)-approximation*algorithm*for*maximum**weight*matching in graphs with small edge*weights*due to Duan*and*Pettie then we obtain (1 − ... Acknowledgments The authors are grateful to anonymous referees for valuable comments on*a*preliminary version*of*the paper. ...##
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Instantly decodable network coding for real-time device-to-device communications

2016
*
EURASIP Journal on Advances in Signal Processing
*

Due to the complexity

doi:10.1186/s13634-015-0293-z
fatcat:xoqmm7sfdnhmvct7cjxkwgycfq
*of*discovering such*maximum*clique, the paper presents*a**fast*selection*algorithm*. ... The complexity*of*the solution is reduced by first proposing*efficient*methods for the construction, the update,*and*the dimension*reduction**of*the IDNC graph. ... This paper proposes to reduce the complexity*of*the delay*reduction**algorithms*through*efficient*construction, update,*and*dimension*reduction**of*the solution. ...##
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Recent Advances in Practical Data Reduction
[article]

2020
*
arXiv
*
pre-print

Over the last two decades, significant advances have been made in the design

arXiv:2012.12594v3
fatcat:vpsucno5cvgotovfiihkyyytba
*and*analysis*of*fixed-parameter*algorithms*for*a*wide variety*of*graph-theoretic problems. ... We survey recent trends in data*reduction*engineering results for selected problems. ... Partially supported by DFG grants MN 59/1-1*and*SCHU 2567/1-2. ...##
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Page 467 of Mathematical Reviews Vol. , Issue 88a
[page]

1988
*
Mathematical Reviews
*

Summary: “Parallel

*algorithms*are given for finding*a**maximum**weighted*clique,*a**maximum**weighted**independent**set*,*a*minimum clique cover,*and**a*minimum*weighted*dominating*set**of*an inter- val graph. ... Diana Schmidt (Karlsruhe) 88a:68043 68Q20 05C35 68R10 Alon, Noga (1-MIT); Babai, Laszl6 (1-CHI); Itai, Alon (1-CHI)*A**fast**and*simple randomized parallel*algorithm*for the maximal*independent**set*problem ...##
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Fast and simple approximation algorithms for maximum weighted independent set of links

2014
*
IEEE INFOCOM 2014 - IEEE Conference on Computer Communications
*

Finding

doi:10.1109/infocom.2014.6848102
dblp:conf/infocom/WanJDDF14
fatcat:fd7jdo2lwrbufag4c4czkrdvie
*a**maximum*-*weighted**independent**set**of*links is*a*fundamental problem in wireless networking*and*has broad applications in various wireless link scheduling problems. ... In this paper, we present*a*number*of**fast**and*simple approximation*algorithms*under the general protocol interference model. ... Given*a*subset*of**and**a*positive*weight*function on , the problem*of*finding an*independent*subset (abbreviated with IS)*of*with*maximum*total*weight*∑ ∈ ( ) is known as*Maximum**Weighted**Independent**Set*...##
###
Towards Nearly-Linear Time Algorithms for Submodular Maximization with a Matroid Constraint

2019
*
International Colloquium on Automata, Languages and Programming
*

We develop

doi:10.4230/lipics.icalp.2019.54
dblp:conf/icalp/EneN19a
fatcat:ctcnzhg3zzgdfb6l5mpw7ffvw4
*a*new*algorithm*for*a*general matroid constraint with*a*1 − 1/e − approximation that achieves*a**fast*running time provided we have*a**fast*data structure for maintaining an approximately*maximum*...*weight*base in the matroid through*a*sequence*of*decrease*weight*operations. ... Suppose that we have*a*data structure for maintaining*a**maximum**weight*base*and**independent**set*as described above. ...##
###
Parallel computation on interval graphs using PC clusters: Algorithms and experiments
[chapter]

1998
*
Lecture Notes in Computer Science
*

interval covering,

doi:10.1007/bfb0057943
fatcat:2lltogfmgrelfpyvmlw22r2yhy
*maximum**independent**set**and*minimum dominating*set*. ... on*a**Fast*Ethernet based PC cluster. ... In the*maximum**weighted*clique problem for an interval graph, we want to know the*maximum**weight**of*such*a**set*, given*weights*p(I 0 > 0 on the intervals,*and*identify*a**maximum**weighted*clique by marking ...##
###
Scalable Graph Algorithms
[article]

2019
*
arXiv
*
pre-print

Designing

arXiv:1912.00245v1
fatcat:mop2e6pqtnbr7irkrakraael6a
*and*evaluating scalable graph*algorithms*to handle these data*sets*is*a*crucial task on the road to understanding the underlying systems. ... This habilitation thesis is*a*summary*a*broad spectrum*of*scalable graph*algorithms*that I developed over the last six years with many coauthors. ... Such*a**set*is called*a**maximum**weight**independent**set*(MWIS). ...##
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Matching is as easy as matrix inversion

1987
*
Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87
*

We show applications

doi:10.1145/28395.383347
dblp:conf/stoc/MulmuleyVV87
fatcat:jupztmizqfdzpjsvcatu37roqi
*of*this lemma to parallel computation*and*randomized*reductions*. ...*A*new*algorithm*for finding*a**maximum*matching in*a*general graph is presented; its special feature being that the only computationally non-trivial step required in its execution is the inversion*of**a*... The*reduction*is as follows. First assign*a*random*and**independent**weight*w(v) to each vertex VEV, chosen from [l, 2n1, where n = IVI. ...##
###
Matching is as easy as matrix inversion

1987
*
Combinatorica
*

We show applications

doi:10.1007/bf02579206
fatcat:a6qd6xuqcbhufgqnk2sn4vyesa
*of*this lemma to parallel computation*and*randomized*reductions*. ...*A*new*algorithm*for finding*a**maximum*matching in*a*general graph is presented; its special feature being that the only computationally non-trivial step required in its execution is the inversion*of**a*... The*reduction*is as follows. First assign*a*random*and**independent**weight*w(v) to each vertex VEV, chosen from [l, 2n1, where n = IVI. ...##
###
On complexity of optimized crossover for binary representations
[article]

2007
*
arXiv
*
pre-print

We study

arXiv:0705.3766v1
fatcat:xhprpsxg75gs7p73ry3xnow7ze
*a*connection between the OGTC for linear Boolean programming problem*and*the*maximum**weight**independent**set*problem on 2-colorable hypergraph*and*prove the NP-hardness*of*several special cases ... By means*of**efficient**reductions**of*the optimized gene transmitting crossover problems (OGTC) we show the polynomial solvability*of*the OGTC for the*maximum**weight**set*packing problem, the minimum*weight*... This simplified*reduction*is identical to the one in Proposition 1 if*A*is an incidence matrix*of*the ordinary graph G given for the*maximum**weight**independent**set*problem*and*b = e. ...##
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A fast CU Size Decision Algorithm for 3D-HEVC

2016
*
MATEC Web of Conferences
*

To speed up the encoding process for the dependent texture views, we propose

doi:10.1051/matecconf/20166107006
fatcat:shtoegnnfzhkjivs4tsnz5jcie
*a**fast*CU depth range selection*algorithm*by jointly making use*of*the inter-view*and*temporal-spatial correlations. ... Firstly, adaptive correlation*weights*are proposed to predict coding unit(CU) depth range*and*skip some specific depth levels rarely used in*independent*view, the previous frame*and*neighboring CUs. ... Based on the characteristics*of*3D video, we propose*a*depth range selection*algorithm*based on adaptive*weights*using split complexity(SC), which is defined as follows: is the*maximum*value*of*depth level ...##
###
The maximum clique problem

1994
*
Journal of Global Optimization
*

In this paper we present

doi:10.1007/bf01098364
fatcat:qmknkbopunaijoi7joaaab3rey
*a*survey*of*results concerning*algorithms*, complexity,*and*applications*of*the*maximum*clique problem. ... We discuss enumerative*and*exact*algorithms*, heuristics,*and**a*variety*of*other proposed methods. An up to date bibliography on the*maximum*clique*and*related problems is also provided. ... The size*of**a**maximum**independent**set*is the stability number*of*G (denoted by*a*(G)). The*maximum**weight**independent**set*problem asks for an*independent**set**of**maximum**weight*. ...
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