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Algorithms to Approximate Column-Sparse Packing Problems [article]

Brian Brubach, Karthik Abinav Sankararaman, Aravind Srinivasan, Pan Xu
2019 arXiv   pre-print
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization.  ...  We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation algorithms for some well-known families of such problems.  ...  We would like to thank the anonymous reviewers for valuable comments on this paper.  ... 
arXiv:1711.02724v6 fatcat:d6yiu6bqbjdslmvosgjgrqlmqe

Algorithms to Approximate Column-Sparse Packing Problems [chapter]

Brian Brubach, Karthik A. Sankararaman, Aravind Srinivasan, Pan Xu
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization.  ...  We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation algorithms for some well-known families of such problems.  ...  We would like to thank the anonymous reviewers for valuable comments.  ... 
doi:10.1137/1.9781611975031.22 dblp:conf/soda/BrubachSSX18 fatcat:xluk5r7or5hvdbvodypvmqifgy

Packing Interdiction and Partial Covering Problems [chapter]

Michael Dinitz, Anupam Gupta
2013 Lecture Notes in Computer Science  
There is a polynomial time O(log q · min{q, log k})-approximation algorithm for the (k, q)-Packing Interdiction problem.  ...  This is a corollary of our main result, an O(log q · min{q, log k})-approximation to Packing Interdiction where q is the row-sparsity of the packing LP and k is the column-sparsity.  ...  When the matrix A is k-row-sparse and q-column-sparse we call this problem (k, q)-Packing Interdiction (or (k, q)-PI).  ... 
doi:10.1007/978-3-642-36694-9_14 fatcat:ztrpcm5zkfdtvcjjq3zrz64ii4

Applications of sparse approximation in communications

A.C. Gilbert, J.A. Tropp
2005 Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.  
Sparse approximation problems abound in many scientific, mathematical, and engineering applications.  ...  For MIMO wireless communication channels, we construct simultaneous sparse approximation problems and demonstrate that our algorithms can both decode the transmitted signals and estimate the channel parameters  ...  The algorithms for sparse approximation provide provable decoding algorithms for this problem.  ... 
doi:10.1109/isit.2005.1523488 dblp:conf/isit/GilbertT05 fatcat:56gtnqua6rhrlmwbi5yr6dxwt4

Approximating low-congestion routing and column-restricted packing problems

Alok Baveja, Aravind Srinivasan
2000 Information Processing Letters  
packing problems.  ...  We contribute to a body of research asserting that the fractional and integral optima of column-sparse integer programs are "nearby".  ...  The best general provable approximations to-date for such packing problems start by considering the linear programming (LP) relaxation where each x j is relaxed to be a real lying in [0, d j ]; the objective  ... 
doi:10.1016/s0020-0190(00)00033-8 fatcat:b65jr7j6jzcxjkcop5qiqksi3m

On k-Column Sparse Packing Programs [chapter]

Nikhil Bansal, Nitish Korula, Viswanath Nagarajan, Aravind Srinivasan
2010 Lecture Notes in Computer Science  
We give an (ek+o(k))-approximation algorithm for k-column sparse PIPs, improving on recent results of k^2· 2^k and O(k^2).  ...  We also show that the integrality gap of our linear programming relaxation is at least 2k-1; it is known that k-column sparse PIPs are Ω(k/ k)-hard to approximate.  ...  We thank Jan Vondrak and Chandra Chekuri for pointing out an error in the original proof of Theorem 5.5, which prompted us to prove Theorem 5.3.  ... 
doi:10.1007/978-3-642-13036-6_28 fatcat:2vct55fkrnehbnhl2ofgi2tiry

Approximability of Sparse Integer Programs [article]

David Pritchard, Deeparnab Chakrabarty
2010 arXiv   pre-print
Second, for packing integer programs max cx: Ax <= b, 0 <= x <= d where A has at most k nonzeroes per column, we give a (2k^2+2)-approximation algorithm.  ...  In addition, we obtain improved approximations for the second problem when k=2, and for both problems when every A_ij is small compared to b_i.  ...  We would like to thank Glencora Borradaile, Christina Boucher, Stephane Durocher, Jochen Könemann and Christos Koufogiannakis for helpful discussions, and the ESA referees for useful feedback.  ... 
arXiv:0904.0859v5 fatcat:vvivwsb7nrhzvfwhpwmlbwgvly

Techniques for parallel manipulation of sparse matrices

Clyde P. Kruskal, Larry Rudolph, Marc Snir
1989 Theoretical Computer Science  
We consider the following problems: matrix addition, matrix multiplication, row and column permutation, matrix transpose, matrix vector multiplication, and Gaussian elimination.  ...  New techniques are presented forthe manipulation of sparse matrices on parallel MIMD computers.  ...  These methods were used to develop algorithms that efficiently solve sparse graph problems [6, 171.  ... 
doi:10.1016/0304-3975(89)90058-3 fatcat:xsaxgzwxhjabvjp4zgsfawlwn4

Page 2765 of Mathematical Reviews Vol. , Issue 86f [page]

1986 Mathematical Reviews  
In this paper, the authors propose a new quasi-Newton method which uses sparse triple factorization of an approximation to the sparse Hessian matrix.  ...  At each step of the algorithm, they deter- mine a new column and a corresponding row of the approximate Hessian matrix and update its triple factorization by using a rank- two updating scheme.  ... 

Iterative Packing for Demand and Hypergraph Matching [chapter]

Ojas Parekh
2011 Lecture Notes in Computer Science  
We apply iterative packing to generalized matching problems including demand matching and k-column-sparse column-restricted packing (k-CS-PIP) and obtain approximation algorithms that essentially settle  ...  Although iterative rounding methods have been applied to packing problems, no single method has emerged that matches the effectiveness and simplicity afforded by the covering case.  ...  It is conceivable that one may also develop an analogue of iterative packing for covering that appeals to approximate convex decompositions.  ... 
doi:10.1007/978-3-642-20807-2_28 fatcat:exxoj3fx4zbfviz6eumbmph43y

Approximability of Sparse Integer Programs

David Pritchard, Deeparnab Chakrabarty
2010 Algorithmica  
Second, for packing integer programs {max cx : Ax ≤ b, 0 ≤ x ≤ d} where A has at most k nonzeroes per column, we give a (2k 2 + 2)-approximation algorithm.  ...  In addition, we obtain improved approximations for the second problem when k = 2, and for both problems when every A ij is small compared to b i .  ...  Acknowledgement We would like to thank Glencora Borradaile, Christina Boucher, Stephane Durocher, Jochen Könemann and Christos Koufogiannakis for helpful discussions, and the ESA and Algorithmica referees  ... 
doi:10.1007/s00453-010-9431-z fatcat:h4te5eiug5cdvnhr5asr66uyby

Efficient Submodular Function Maximization under Linear Packing Constraints [article]

Yossi Azar, Iftah Gamzu
2012 arXiv   pre-print
We study the problem of maximizing a monotone submodular set function subject to linear packing constraints.  ...  We also study the special setting in which the matrix A is binary and k-column sparse. A k-column sparse matrix has at most k non-zero entries in each of its column.  ...  Acknowledgments: The authors thank Chandra Chekuri, Ilan Cohen, Gagan Goel, and Jan Vondrák for valuable discussions on topics related to the subject of this study.  ... 
arXiv:1007.3604v2 fatcat:jejfewz2nngq7oi7bc4qudlupi

Solving Packing Integer Programs via Randomized Rounding with Alterations

Nikhil Bansal, Nitish Korula, Viswanath Nagarajan, Aravind Srinivasan
2012 Theory of Computing  
We also generalize our result to the case of maximizing non-negative monotone submodular functions over k-column sparse packing constraints, and obtain an e 2 k e−1 + o(k) -approximation algorithm.  ...  We give an (ek + o(k))-approximation algorithm for k-column sparse PIPs, improving over previously known O(k 2 )-approximation ratios.  ...  Our thanks also to the IPCO and ToC referees for their helpful suggestions, which improved the presentation of the paper.  ... 
doi:10.4086/toc.2012.v008a024 dblp:journals/toc/BansalKNS12 fatcat:bxd4am3gyzg2hefdvjvmdf5nam

Online Multidimensional Packing Problems in the Random-Order Model

David Naori, Danny Raz, Michael Wagner
2019 International Symposium on Algorithms and Computation  
ACM Subject Classification Theory of computation → Packing and covering problems; Theory of computation → Online algorithms  ...  Furthermore, our algorithm improves upon the best-known competitive-ratio for the online (one-dimensional) generalized assignment problem and the online knapsack problem.  ...  It is also very interesting to understand whether the new theoretical algorithm provides practical value for cloud resource allocation, where the value of d is a small constant (2 or 3).  ... 
doi:10.4230/lipics.isaac.2019.10 dblp:conf/isaac/NaoriR19 fatcat:nynljwfm7rghbd4e6umutmkz44

A Compressed Diagonals Remapping Technique for Dynamic Data Redistribution on Banded Sparse Matrix [chapter]

Ching-Hsien Hsu, Kun-Ming Yu
2003 Lecture Notes in Computer Science  
The second advantage of the present techniques is the achievement of optimal packing/unpacking stages consequent upon the consecutive attribute of column elements in a compressed diagonal matrix.  ...  to redistribute data in the banded sparse matrix.  ...  Since a sparse vector of matrix M (identical to matrix column of M CD ) will be distributed to the same computing node, we can reduce the problem further to one-dimensional BLOCK-CYCLIC redistribution  ... 
doi:10.1007/3-540-37619-4_8 fatcat:chcwbycbnzd3pdijtb42mibvta
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