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

Fabrizio Grandoni, Tomasz Kociumaka, Michał Włodarczyk
2014 arXiv   pre-print
On the other hand, the best known 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 .  ... 
arXiv:1405.0456v1 fatcat:m3bydxe435btlbfumz2vijz7ai

An LP-rounding 22-approximation for restricted maximum acyclic subgraph

Fabrizio Grandoni, Tomasz Kociumaka, Michał Włodarczyk
2015 Information Processing Letters  
In this paper we present a non-trivial LP-rounding algorithm for RMAS with approximation ratio 22 ≈ 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.  ... 
doi:10.1016/j.ipl.2014.09.008 fatcat:qg73qgn3ezamli6ea7n6jkth74

On Hardness of Pricing Items for Single-Minded Bidders [chapter]

Rohit Khandekar, Tracy Kimbrel, Konstantin Makarychev, Maxim Sviridenko
2009 Lecture Notes in Computer Science  
The best known 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.  ... 
doi:10.1007/978-3-642-03685-9_16 fatcat:uugmry5ovzd63ael4memdhepru

On the Approximability of Digraph Ordering [chapter]

Sreyash Kenkre, Vinayaka Pandit, Manish Purohit, Rishi Saket
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 √ 22 + 1 ≈ 2.344 approximation for it, improving on the 22 ≈ 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  ... 
doi:10.1007/978-3-662-48350-3_66 fatcat:eziyzfrakfc2fchcdgjgmpqfzy

On the Approximability of Digraph Ordering

Sreyash Kenkre, Vinayaka Pandit, Manish Purohit, Rishi Saket
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 √ 22 + 1 ≈ 2.344 approximation for it, improving on the 22 ≈ 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  ... 
doi:10.1007/s00453-016-0227-7 fatcat:mfpulgouibaglawrnun4cjgeru

On the Approximability of Digraph Ordering [article]

Sreyash Kenkre, Vinayaka Pandit, Manish Purohit, Rishi Saket
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  ... 
arXiv:1507.00662v1 fatcat:izonkxu2x5dijicqixmku4g7mi

Approximating Directed Steiner Problems via Tree Embedding [article]

Bundit Laekhanukit
2016 arXiv   pre-print
If 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.  ... 
arXiv:1511.06559v3 fatcat:mt4v3j7oo5hrxhetiypn6gyvpq

Virtual Network Embedding Approximations: Leveraging Randomized Rounding [article]

Matthias Rost, Stefan Schmid
2018 arXiv   pre-print
Our 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] .  ... 
arXiv:1803.03622v2 fatcat:l7k2izg4sbf3fmfghknd7tsoai

Task Distributions on Multiprocessor Systems [chapter]

Evgeny V. Shchepin, Nodari N. Vakhania
2000 Lecture Notes in Computer Science  
In [1] is also proved a general 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.  ... 
doi:10.1007/3-540-44929-9_10 fatcat:xjm2bsuybvbmzcoa5rbqhsxhgm

Edge-disjoint paths revisited

Chandra Chekuri, Sanjeev Khanna
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.  ... 
doi:10.1145/1290672.1290683 fatcat:7vyztvdf7rfwxcnfdfkdgzhjbe

Virtual Network Embedding Approximations: Leveraging Randomized Rounding

Matthias Rost, Stefan Schmid
2018 2018 IFIP Networking Conference (IFIP Networking) and Workshops  
Our 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] .  ... 
doi:10.23919/ifipnetworking.2018.8696623 dblp:conf/networking/Rost018a fatcat:vxa3phxwanhczf3djh4ei26jlq

Maximum Coverage with Cluster Constraints: An LP-Based Approximation Technique [chapter]

Guido Schäfer, Bernard G. Zweers
2021 Lecture Notes in Computer Science  
We apply our technique to derive 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  ... 
doi:10.1007/978-3-030-80879-2_5 fatcat:4xbiq3nsk5eillsxsbzpugxs5m

Maximum Coverage with Cluster Constraints: An LP-Based Approximation Technique [article]

Guido Schäfer, Bernard G. Zweers
2020 arXiv   pre-print
We apply our technique to derive 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  ... 
arXiv:2012.04420v1 fatcat:bh367i7y3rgqfgwknxmnuejf5q

Integrality gaps for Sherali-Adams relaxations

Moses Charikar, Konstantin Makarychev, Yury Makarychev
2009 Proceedings of the 41st annual ACM symposium on Symposium on theory of computing - STOC '09  
Using this, we construct 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.  ... 
doi:10.1145/1536414.1536455 dblp:conf/stoc/CharikarMM09 fatcat:dkanhr3ge5hvpcuhdulgfcmrrm

Finding Independent Sets in Unions of Perfect Graphs

Venkatesan T. Chakaravarthy, Vinayaka Pandit, Sambuddha Roy, Yogish Sabharwal, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
The 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.  ... 
doi:10.4230/lipics.fsttcs.2010.251 dblp:conf/fsttcs/ChakaravarthyPRS10 fatcat:qsg7amfhkbbdbcd7ixpapx54ma
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