A new approach to the maximum-flow problem
Journal of the ACM (JACM)
The maximum concurrent flow problem
Journal of the ACM (JACM)
Very simple methods for all pairs network flow analysis
SIAM Journal on Computing
On the design of approximation algorithms for a class of graph problems
On the design of approximation algorithms for a class of graph problems
Fast approximation algorithms for multicommodity flow problems
Selected papers of the 23rd annual ACM symposium on Theory of computing
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Coordination complexity of parallel price-directive decomposition
Mathematics of Operations Research
Fast deterministic approximation for the multicommodity flow problem
Mathematical Programming: Series A and B
Randomized rounding without solving the linear program
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
Approximation algorithms for minimum-cost k-vertex connected subgraphs
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Faster approximation schemes for fractional multicommodity flow problems
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Fast Approximation Algorithms for Fractional Steiner Forest and Related Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Sequential and Parallel Algorithms for Mixed Packing and Covering
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
An Iterative Rounding 2-Approximation Algorithm for the Element Connectivity Problem
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Distributed approximation: a survey
ACM SIGACT News
Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
Combinatorial approaches to QoS scheduling in multichannel infrastructure wireless networks
WICON '06 Proceedings of the 2nd annual international workshop on Wireless internet
Faster and simpler approximation algorithms for mixed packing and covering problems
Theoretical Computer Science
Online Primal-Dual Algorithms for Covering and Packing
Mathematics of Operations Research
The Design of Competitive Online Algorithms via a Primal: Dual Approach
Foundations and Trends® in Theoretical Computer Science
Provably good and practically efficient algorithms for CMP dummy fill
Proceedings of the 46th Annual Design Automation Conference
Approximation schemes for deal splitting and covering integer programs with multiplicity constraints
Theoretical Computer Science
Online primal-dual algorithms for covering and packing problems
ESA'05 Proceedings of the 13th annual European conference on Algorithms
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Approximation algorithms for mixed fractional packing and covering problems
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Approximation schemes for deal splitting and covering integer programs with multiplicity constraints
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Feasible and accurate algorithms for covering semidefinite programs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
An approximation algorithm for the general mixed packing and covering problem
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
An efficient method for gradient-aware dummy fill synthesis
Integration, the VLSI Journal
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We present the first combinatorial approximation scheme for mixed positive packing and covering linear programs that yields a pure approximation guarantee. Our algorithm returns solutions that simultaneously satisfy general positive covering constraints and packing constraints that are variable upper bounds. The returned solution has positive linear objective function value at most 1 + ε times the optimal value.Our approximation scheme is based on Lagrangian-relaxation methods. Previous such approximation schemes for mixed packing and covering problems does not simultaneously satisfy packing and covering constraints exactly. We show how to exactly satisfy general positive covering constraints simultaneously with variable upper bounds.A natural set of problems that our work addresses are linear programs for various network design problems: generalized Steiner network, vertex connectivity, directed connectivity, capacitated network design, group Steiner forest. These are all NP-hard problems for which there are approximation algorithms that round the solution to the corresponding linear program. Solving the linear program is often the computational bottleneck in these problems, and thus a fast approximation scheme for the LP relaxation means faster approximation algorithms.For the special case of survivable network design, we introduce a new modification of the push-relabel maximum flow algorithm that allows us to perform each iteration in amortized O(m + n log n) time, instead of one maximum flow per iteration that is implied by the straight forward adaptation of our general algorithm. (m is the number of edges and n is the number of vertices in the network.) In conjunction with an observation that reduces the number of iterations to {log n for f0} constraint matrices, the modification allows us to obtain an algorithm that is faster than existing exact or approximate algorithms by a factor of at least O(m) and by a factor of O(m log n) if the number of demand pairs is Ω(n).