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An LP-Rounding 2√(2) Approximation for Restricted Maximum Acyclic Subgraph
[article]

2014
*
arXiv
*
pre-print

On the other hand, the best known

arXiv:1405.0456v1
fatcat:m3bydxe435btlbfumz2vijz7ai
*2*inapproximability result is due to a reduction from a special case of RMAS. In this paper we present*an*improved*LP*-*rounding**2*√(*2*)*approximation**for*RMAS. ... In this paper we consider a generalization of MAS, the*Restricted**Maximum**Acyclic**Subgraph*problem (RMAS), where each node is associated with a list of integer labels, and we have to find a labeling of ... In the*Restricted**Maximum**Acyclic**Subgraph*problem (RMAS) we are given the same input as*for*MAS, plus a set L v of integer labels*for*each node v 1 . ...##
###
An LP-rounding 22-approximation for restricted maximum acyclic subgraph

2015
*
Information Processing Letters
*

In this paper we present a non-trivial

doi:10.1016/j.ipl.2014.09.008
fatcat:qg73qgn3ezamli6ea7n6jkth74
*LP*-*rounding*algorithm*for*RMAS with*approximation*ratio*2*√*2*≈ 2.828. ... In the classical*Maximum**Acyclic**Subgraph*problem (MAS), given a directed-edge weighted graph, we are required to find*an*ordering of the nodes that maximizes the total weight of forward-directed edges ... Acknowledgements This work has been partially supported by the ERC Starting Grant NEWNET 279352 and by Foundation*for*Polish Science grant HOMING PLUS/2012-6/*2*. ...##
###
On Hardness of Pricing Items for Single-Minded Bidders
[chapter]

2009
*
Lecture Notes in Computer Science
*

The best known

doi:10.1007/978-3-642-03685-9_16
fatcat:uugmry5ovzd63ael4memdhepru
*approximation*algorithm, by Balcan and Blum, gives a 4-*approximation*[*2*]. We show that there is indeed a gap of 4*for*the combinatorial upper bound used in their analysis. ... We hope that our techniques will be helpful*for*obtaining stronger hardness of*approximation*bounds*for*this problem. * ... In such a case, they gave*an**LP*-*rounding*algorithm that yields*an**approximation*of 6+ √*2*5+ √*2*≈ 1.15. They also showed a matching integrality gap*for*these instances. ...##
###
On the Approximability of Digraph Ordering
[chapter]

2015
*
Lecture Notes in Computer Science
*

*For*different values of k, this reduces to

*maximum*

*acyclic*

*subgraph*(k = n), and Max-DiCut (k =

*2*). ... We prove

*an*

*LP*

*rounding*based 4 √

*2*√

*2*+ 1 ≈ 2.344

*approximation*

*for*it, improving on the

*2*√

*2*≈ 2.828

*approximation*recently given by Grandoni et al. [7]. ... Introduction One of the most well studied combinatorial problems on directed graphs (digraphs) is the

*Maximum*

*Acyclic*

*Subgraph*problem (MAS): given

*an*n-vertex digraph, find a

*subgraph*3 of

*maximum*number ...

##
###
On the Approximability of Digraph Ordering

2016
*
Algorithmica
*

*For*different values of k, this reduces to

*maximum*

*acyclic*

*subgraph*(k = n), and Max-DiCut (k =

*2*). ... We prove

*an*

*LP*

*rounding*based 4 √

*2*√

*2*+ 1 ≈ 2.344

*approximation*

*for*it, improving on the

*2*√

*2*≈ 2.828

*approximation*recently given by Grandoni et al. [7]. ... Introduction One of the most well studied combinatorial problems on directed graphs (digraphs) is the

*Maximum*

*Acyclic*

*Subgraph*problem (MAS): given

*an*n-vertex digraph, find a

*subgraph*3 of

*maximum*number ...

##
###
On the Approximability of Digraph Ordering
[article]

2015
*
arXiv
*
pre-print

*For*different values of k, this reduces to

*Maximum*

*Acyclic*

*Subgraph*(k=n), and Max-Dicut (k=

*2*). ... We prove

*an*

*LP*

*rounding*based 4√(

*2*)/(√(

*2*)+1) ≈ 2.344

*approximation*

*for*it, improving on the

*2*√(

*2*)≈ 2.828

*approximation*recently given by Grandoni et al. ... Introduction One of the most well studied combinatorial problems on directed graphs (digraphs) is the

*Maximum*

*Acyclic*

*Subgraph*problem (MAS): given

*an*n-vertex digraph, find a

*subgraph*3 of

*maximum*number ...

##
###
Approximating Directed Steiner Problems via Tree Embedding
[article]

2016
*
arXiv
*
pre-print

If

arXiv:1511.06559v3
fatcat:mt4v3j7oo5hrxhetiypn6gyvpq
*an*input graph is not*acyclic*, the complexity status of k-DST is not known even*for*a very strict special case that k=*2*and |T| =*2*. ... [SODA'12, TALG'14] and by Laekhanukit [SODA'14], there was no known non-trivial*approximation*algorithm*for*k-DST*for*k >=*2*even in the special case that*an*input graph is directed*acyclic*and has a constant ... We also thank Zachary Friggstad*for*useful discussions. ...##
###
Virtual Network Embedding Approximations: Leveraging Randomized Rounding
[article]

2018
*
arXiv
*
pre-print

Our

arXiv:1803.03622v2
fatcat:l7k2izg4sbf3fmfghknd7tsoai
*approximation*is based on the randomized*rounding*of Linear Programming (*LP*) solutions. ... Proving performance guarantees of our*rounding*scheme, we obtain the first*approximation*algorithm*for*the VNEP in the resource augmentation model. ... We thank Elias Döhne, Alexander Elvers, and Tom Koch*for*their significant contribution to our implementation [21] . ...##
###
Task Distributions on Multiprocessor Systems
[chapter]

2000
*
Lecture Notes in Computer Science
*

In [1] is also proved a general

doi:10.1007/3-540-44929-9_10
fatcat:xjm2bsuybvbmzcoa5rbqhsxhgm
*rounding*theorem, which allows to construct in polynomial time 1-job*approximations*to the optimum, i.e. schedules with*an*absolute bound equal to the largest job processing ... In [1] was suggested a polynomial 2approximation algorithm*for*this problem. It was also proved that there can exist no polynomial 1.5-*approximation*algorithm unless P = NP . ... Let P 1 , P*2*, . . . , P k be connected*subgraphs*of*an**acyclic*graph G, having in common at most one node. ...##
###
Edge-disjoint paths revisited

2007
*
ACM Transactions on Algorithms
*

*For*ayclic graphs we give

*an*O(x/nlogn )

*approximation*via

*LP*

*rounding*. These are the first sub-linear

*approximation*ratios

*for*EDP. ... The

*approximability*of the

*maximum*edge disjoint paths problem (EDP) in directed graphs was seemingly settled by the fl(ml/

*2*-e)-hardness result of Guruswami et al. [10] and the O(x/~ )

*approximation*achievable ... Acknowledgments: We thank Anupam Gupta and Bruce Shepherd

*for*useful discussions and clarifications. ...

##
###
Virtual Network Embedding Approximations: Leveraging Randomized Rounding

2018
*
2018 IFIP Networking Conference (IFIP Networking) and Workshops
*

Our

doi:10.23919/ifipnetworking.2018.8696623
dblp:conf/networking/Rost018a
fatcat:vxa3phxwanhczf3djh4ei26jlq
*approximation*is based on the randomized*rounding*of Linear Programming (*LP*) solutions. ... Proving performance guarantees of our*rounding*scheme, we obtain the first*approximation*algorithm*for*the VNEP in the resource augmentation model. ... We thank Elias Döhne, Alexander Elvers, and Tom Koch*for*their significant contribution to our implementation [20] . ...##
###
Maximum Coverage with Cluster Constraints: An LP-Based Approximation Technique
[chapter]

2021
*
Lecture Notes in Computer Science
*

We apply our technique to derive

doi:10.1007/978-3-030-80879-2_5
fatcat:4xbiq3nsk5eillsxsbzpugxs5m
*approximation*algorithms*for*MCPC. To this aim, we develop*an**LP*-based 1*2*(1 − 1 e )-*approximation*algorithm*for*MCPK by adapting the pipage*rounding*technique. ... By using*an**LP*-based*approximation*algorithm*for*the original problem, we can then obtain*an*effective*rounding*scheme*for*the problem, which only loses a small fraction in the*approximation*guarantee. ... Algorithm*2*is a 1 3 -*approximation*algorithm*for*MKPC. 1*2*-*Approximation**for*MKPC with Isolation Property We derive*an*iterative*rounding*1*2*-*approximation*algorithm*for*instances of MKPC that satisfy ...##
###
Maximum Coverage with Cluster Constraints: An LP-Based Approximation Technique
[article]

2020
*
arXiv
*
pre-print

We apply our technique to derive

arXiv:2012.04420v1
fatcat:bh367i7y3rgqfgwknxmnuejf5q
*approximation*algorithms*for*MCPC. To this aim, we develop*an**LP*-based 1/*2*(1-1/e)-*approximation*algorithm*for*MCPK by adapting the pipage*rounding*technique. ... By using*an**LP*-based*approximation*algorithm*for*the original problem, we can then obtain*an*effective*rounding*scheme*for*the problem, which only loses a small fraction in the*approximation*guarantee. ... Algorithm*2*is a 1 3 -*approximation*algorithm*for*MKPC. 1*2*-*Approximation**for*MKPC with Isolation Property We derive*an*iterative*rounding*1*2*-*approximation*algorithm*for*instances of MKPC that satisfy ...##
###
Integrality gaps for Sherali-Adams relaxations

2009
*
Proceedings of the 41st annual ACM symposium on Symposium on theory of computing - STOC '09
*

Using this, we construct

doi:10.1145/1536414.1536455
dblp:conf/stoc/CharikarMM09
fatcat:dkanhr3ge5hvpcuhdulgfcmrrm
*2*− ε gap examples*for**Maximum**Acyclic**Subgraph*that rules out any family of linear constraints with support at most n δ . ...*For*MAX CUT and Vertex Cover, these show that even n δ*rounds*of Sherali-Adams do not yield a better than*2*− ε*approximation*. ... This allows us to obtain*an*integrality gap*for*the Sherali-Adams relaxation of*Maximum**Acyclic**Subgraph*. ...##
###
Finding Independent Sets in Unions of Perfect Graphs

2010
*
Foundations of Software Technology and Theoretical Computer Science
*

The

doi:10.4230/lipics.fsttcs.2010.251
dblp:conf/fsttcs/ChakaravarthyPRS10
fatcat:qsg7amfhkbbdbcd7ixpapx54ma
*maximum*independent set problem (MaxIS) on general graphs is known to be NP-hard to*approximate*within a factor of n 1− ,*for*any > 0. ... In this context,*an*interesting question is that of computing the*maximum*independent set in a graph that can be expressed as the union of a small number of graphs from*an*easy class. ... Notice that I is*an*independent set in both G 1 and G*2*, and hence, it is*an*independent set in G. Our O( √ n)-*approximation*uses the*LP**rounding*approach. ...
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