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Approximation Algorithms for Mixed Fractional Packing and Covering Problems
[chapter]
2005
Lecture Notes in Computer Science
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The main contribution is that the algorithm solves the general mixed fractional packing and covering problem (in contrast to pure fractional packing and covering problems and to the special mixed packing ...
We propose an approximation algorithm based on the Lagrangian or pricedirective decomposition method to compute an¯-approximate solution of the mixed fractional packing and covering problem: find Ü ¾ such ...
Our approximation algorithm In this section we describe the approximation algorithms for the mixed fractional packing and covering problem. ...
doi:10.1007/978-3-540-31833-0_2
fatcat:3zep5zfs6nhl7egm3ihvqirr64
Approximation Algorithms for Mixed Fractional Packing and Covering Problems
[chapter]
IFIP International Federation for Information Processing
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The main contribution is that the algorithm solves the general mixed fractional packing and covering problem (in contrast to pure fractional packing and covering problems and to the special mixed packing ...
We propose an approximation algorithm based on the Lagrangian or pricedirective decomposition method to compute an¯-approximate solution of the mixed fractional packing and covering problem: find Ü ¾ such ...
Our approximation algorithm In this section we describe the approximation algorithms for the mixed fractional packing and covering problem. ...
doi:10.1007/1-4020-8141-3_19
dblp:conf/ifipTCS/Jansen04
fatcat:w4hevlx3kfb6npdf3c4mxu7w7m
Packing Interdiction and Partial Covering Problems
[chapter]
2013
Lecture Notes in Computer Science
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There is a polynomial time O(log q · min{q, log k})-approximation algorithm for the (k, q)-Packing Interdiction problem. ...
we consider approximation algorithms for it. ...
There is a polynomial time α-approximation algorithm for (q, k)-Packing Interdiction if and only if there is a polynomial time α-approximation algorithm for (k, q)-Partial Covering. Proof. ...
doi:10.1007/978-3-642-36694-9_14
fatcat:ztrpcm5zkfdtvcjjq3zrz64ii4
Distributed algorithms for covering, packing and maximum weighted matching
2011
Distributed computing
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This paper gives poly-logarithmic-round, distributed D-approximation algorithms for covering problems with submodular cost and monotone covering constraints (Submodular-cost Covering). ...
Via duality, the paper also gives poly-logarithmic-round, distributed D-approximation algorithms for Fractional Packing linear programs (where D is the maximum number of constraints in which any variable ...
Acknowledgements Thanks to two anonymous referees for their helpful comments. ...
doi:10.1007/s00446-011-0127-7
fatcat:d37gfoitm5bwnego553behrmru
Randomized Rounding without Solving the Linear Program
[article]
2002
arXiv
pre-print
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This paper explores how this bottleneck can be avoided for randomized rounding algorithms for packing and covering problems (linear programs, or mixed integer linear programs, having no negative coefficients ...
This approach can also be used to understand Lagrangian-relaxation algorithms for packing/covering linear programs: such algorithms can be viewed as as (derandomized) randomized-rounding schemes. ...
To demonstrate this, we give approximation algorithms for general packing and covering problems corresponding to integer and noninteger linear programs of small width, including a parallel algorithm for ...
arXiv:cs/0205036v1
fatcat:uqmlbpvj3zaandaj4sbiec2d3y
Approximating Optimal Transport With Linear Programs
2018
ACM-SIAM Symposium on Discrete Algorithms
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faster additive approximation algorithms for optimal transport. ...
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in ...
Acknowledgements We thank Jason Altschuler and Chandra Chekuri for insightful discussions and helpful feedback. ...
doi:10.4230/oasics.sosa.2019.6
dblp:conf/soda/Quanrud19
fatcat:l6hybp6uybgnpl7k3576forlwe
Approximation of a batch consolidation problem
2010
Networks
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The problem is NP-hard and cannot be approximated within 1.0021 of the optimum under the premise, P = NP. However, the problem admits a 3 2 -approximation. ...
We consider the batch consolidation problem of minimizing the number of batches of a finite set of items. ...
Acknowledgments The authors are grateful to the anonymous referees for their helpful comments. ...
doi:10.1002/net.20409
fatcat:gjapr72pwjbszop5yuejqpmkpy
Approximating optimal transport with linear programs
[article]
2018
arXiv
pre-print
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faster additive approximation algorithms for optimal transport. ...
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in ...
We thank Jason Altschuler and Chandra Chekuri for insightful discussions and helpful feedback. ...
arXiv:1810.05957v2
fatcat:4xklx7fffray7km52qzerkj7zy
Knapsack Cover Subject to a Matroid Constraint
2013
Foundations of Software Technology and Theoretical Computer Science
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Our main result proves a 2-factor approximation for this problem. The problem described above falls in the realm of mixed packing covering problems. ...
We also consider packing extensions of certain other covering problems and prove that in such cases it is not possible to derive any constant factor approximations. ...
The submission version contained only a 2-factor approximation for the KCM problem; a reviewer noted that a slight modification ...
doi:10.4230/lipics.fsttcs.2013.275
dblp:conf/fsttcs/ChakaravarthyCNR13
fatcat:gqhr64ln6fhj3goueuo25ufpoq
A Tight Approximation for Submodular Maximization with Mixed Packing and Covering Constraints
2019
International Colloquium on Automata, Languages and Programming
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Motivated by applications in machine learning, such as subset selection and data summarization, we consider the problem of maximizing a monotone submodular function subject to mixed packing and covering ...
Our algorithm is based on a novel enumeration method, which unlike previously known enumeration techniques, can handle both packing and covering constraints. ...
Acknowledgements Joachim Spoerhase and Sumedha Uniyal thank an anonymous reviewer for pointing them to the fact that Theorem 6 also applies to polytopes that are not down-closed, which makes it possible ...
doi:10.4230/lipics.icalp.2019.85
dblp:conf/icalp/MizrachiSSU19
fatcat:wqlfygvyqfdhhni6efmjovmtgq
Fast and Deterministic Approximations for k-Cut
[article]
2018
arXiv
pre-print
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For poly(m,n,k)-time algorithms, the best possible approximation factor is essentially 2 under the small set expansion hypothesis [Manurangsi 2017]. ...
Is there a deterministic algorithm for 2-approximate k-cuts matching the randomized running time of Õ(mk)? The second question qualitatively compares minimum cut to 2-approximate minimum k-cut. ...
Acknowledgements The author thanks Chandra Chekuri for introducing him to the problem and providing helpful feedback, including pointers to the literature for rounding the LP. ...
arXiv:1807.07143v2
fatcat:nytbhcjjlvgtnb4s4bmqgeaaxi
Online Weighted Degree-Bounded Steiner Networks via Novel Online Mixed Packing/Covering
[article]
2017
arXiv
pre-print
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We design an online deterministic integral algorithm with competitive ratio of O(k log m) for the mixed packing/covering integer programs. ...
We then design a generic integral algorithm for solving this restricted family of IPs. We demonstrate a new technique for solving mixed packing/covering integer programs. ...
[5] generalize this method for the fractional mixed packing and covering LPs. ...
arXiv:1704.05811v1
fatcat:nferpbdlxvhtvhnmitx62ix7ji
Fast and Deterministic Approximations for k-Cut
2019
International Workshop on Approximation Algorithms for Combinatorial Optimization
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For poly(m, n, k)-time algorithms, the best possible approximation factor is essentially 2 under the small set expansion hypothesis [37] . ...
We give a deterministic approximation algorithm that computes (2 + )-minimum k-cuts in O m log 3 n/ 2 time, via a (1 + )-approximation for an LP relaxation of k-cut. ...
The standard LP (L) is difficult because it is a mixed packing and covering problem, and fast approximation algorithms for mixed packing and covering problems lead to bicriteria approximations that we ...
doi:10.4230/lipics.approx-random.2019.23
dblp:conf/approx/Quanrud19
fatcat:ffcftkfmlrhypb3bxm7oggfthy
Online Mixed Packing and Covering
[chapter]
2013
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
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We use ideas generated from our result for mixed packing and covering to obtain polylogarithmic-competitive algorithms for these problems. ...
We extend this framework in a fundamental way by demonstrating that it can be used to solve mixed packing and covering LPs online, where packing constraints are given offline and covering constraints are ...
They are used in both offline approximation algorithms for packing and covering problems [11, 18, 21, 24, 25, 26, 30, 32, 33, 39, 41, 42] , and online algorithms for problems with only packing or only ...
doi:10.1137/1.9781611973105.6
dblp:conf/soda/AzarBFP13
fatcat:jfo34xmwqnapnlx5n5jzqp5xvi
Optimizing over Consecutive 1's and Circular 1's Constraints
2006
SIAM Journal on Optimization
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For the "mixed" case with both covering and packing consecutive 1's constraints we present an O(mn) time algorithm. ...
Finally, we show an O(n min{mn, n 2 log n + m log 2 n}) time algorithm for the most general problem of mixed covering and packing case where the constraints are circular. ...
Tamir for discussing an earlier version of this paper and to anonymous referees whose comments and suggestions improved and simplified the presentation of the results in this paper. ...
doi:10.1137/040603048
fatcat:frlhfkp7bbbqncmnzafnyfas7i
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