A parallel approximation algorithm for positive linear programming

@inproceedings{Luby1993APA,
  title={A parallel approximation algorithm for positive linear programming},
  author={M. Luby and N. Nisan},
  booktitle={STOC '93},
  year={1993}
}
We introduce a fast parallel approximation algorithm for the positive linear programming optimization problem, i.e. the special case of the linear programming optimization problem where the input constraint matrix and constraint vector consist entirely of positive entries. The algorithm is elementary, and has a simple parallel implementation that runs in polylog time using a linear number of processors. 
The Parallel Complexity of Positive Linear Programming
TLDR
The problem of exactly solving PLP is P-complete, i.e. the special case of Linear Programming in packing/covering form where the input constraint matrix and constraint vector consist entirely of positive entries. Expand
Positive Linear Programming Extensions: Parallel Complexity and Applications (Research Note)
TLDR
A general class of linear programs that admit efficient parallel approximations and use it for efficient parallel approximation to hard combinatorial optimization problems is proposed. Expand
Positive Linear Programming, Parallel Approximation and PCP's
TLDR
Improved parallel approximation algorithms for Max Sat, Max Directed Cut, and MaxkCSP are developed and a connection between probabilistic proof checking and a restricted version of MaxkKCSP is shown, implying that the approximation algorithm for Max kCSP can be used to prove inclusion in P for certain PCP classes. Expand
Parallel Approximation Algorithms by Positive Linear Programming
  • L. Trevisan
  • Computer Science, Mathematics
  • Algorithmica
  • 1998
TLDR
Improved parallel approximation algorithms for Max Sat, Max Directed Cut, and Maxk CSP are developed and a connection between probabilistic proof checking and a restricted version of MaxkCSP is shown, implying that the approximation algorithm for MaxK CSP can be used to prove inclusion in P for certain PCP classes. Expand
Randomized rounding without solving the linear program
  • N. Young
  • Mathematics, Computer Science
  • SODA '95
  • 1995
TLDR
A new technique called oblivious rounding is introduced a variant of randomized rounding that avoids the bottleneck of first solving the linear program, which yields more efficient algorithms and brings probabilistic methods to bear on a new class of problems. Expand
A Primal-Dual Parallel Approximation Technique Applied to Weighted Set and Vertex Covers
TLDR
The result demonstrates that linear-programming primal-dual approximation techniques can lead to fast, efficient parallel algorithms. Expand
A parallel approximation algorithm for mixed packing and covering semidefinite programs
TLDR
A faster approximation algorithm for positive semidefinite programs with better dependence of the parallel running time on the approximation factor, as compared to that of Jain and Yao [6]. Expand
A Parallelizable Acceleration Framework for Packing Linear Programs
TLDR
An acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints is small compared to the variable dimension, and it provides an approximately optimal solution while running the original solver on a much smaller problem. Expand
A Parallel Approximation Algorithm for Positive Semidefinite Programming
  • Rahul Jain, Penghui Yao
  • Mathematics, Computer Science
  • 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
  • 2011
TLDR
A parallel algorithm is presented, which given an instance of a positive semi definite program of size N and an approximation factor e &gt, 0, runs in (parallel) time poly(1/e) polylog(N), using poly(N) processors, and outputs a value which is within multiplicative factor of (1+ e) to the optimal. Expand
A Distributed Approximation Algorithm for Mixed Packing-Covering Linear Programs
TLDR
An efficient distributed approximation algorithm for solving mixed packing-covering problems which requires a poly-logarithmic number of passes over the input, well-suited for parallel processing on GPUs, in shared-memory architectures, or on small clusters of commodity nodes. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 11 REFERENCES
Fast approximation algorithms for fractional packing and covering problems
TLDR
Fast algorithms that find approximate solutions for a general class of problems, which are called fractional packing and covering problems, are presented, and an important result is a theoretical analysis of the running time of a Lagrangian relaxation based algorithm. Expand
An Introduction to Parallel Algorithms
TLDR
This book provides an introduction to the design and analysis of parallel algorithms, with the emphasis on the application of the PRAM model of parallel computation, with all its variants, to algorithm analysis. Expand
Fast Approximation Algorithms for Fractional Packing and Covering Problems
TLDR
The techniques developed in this paper greatly outperform the general methods in many applications, and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems. Expand
Parallel merge sort
  • R. Cole
  • Computer Science
  • 27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
  • 1986
We give a parallel implementation of merge sort on a CREW PRAM that uses n processors and O(logn) time; the constant in the running time is small. We also give a more complex version of the algorithmExpand
On the hardness of approximating minimization problems
TLDR
It is proved that there is an c >0 such that Graph Coloring cannot be approximated with ratio n’ unless P=NP unless NP is contained in DTIME[nPOIY log ~ ]. Expand
Efficient NC Algorithms for Set Cover with Applications to Learning and Geometry
TLDR
The set cover algorithm is applied to learning theory, providing an NC algorithm for learning the concept class obtained by taking the closure under finite union or finite intersection of any concept class of finite VC dimension which has an NC hypothesis finder. Expand
A deterministic view of random sampling and its use in geometry
  • B. Chazelle, J. Friedman
  • Mathematics, Computer Science
  • [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
  • 1988
TLDR
It is shown how to compute, in polynomial time, a simplicial packing of size O(r/sup d/) that covers d-space, each of whose simplices intersects O(n/r) hyperplanes. Expand
Approximate Max-Flow on Small Depth Networks
  • E. Cohen
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1995
TLDR
A new deterministic algorithm for solving the relaxed problem of computing an $s$-$t$ flow of value at least $(1-\epsilon)$ of the maximum flow, which is in $\NC$ and uses only $O(m)$ processors, a significant improvement over existing parallel algorithms. Expand
Probabilistic construction of deterministic algorithms: Approximating packing integer programs
  • P. Raghavan
  • Computer Science
  • 27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
  • 1986
TLDR
A methodology for converting a probabilistic existence proof to a deterministic approximation algorithm that mimics the existence proof in a very strong sense is developed. Expand
Parallel Prefix Computation
TLDR
A recurstve construction is used to obtain a product circuit for solving the prefix problem and a Boolean clrcmt which has depth 2[Iog2n] + 2 and size bounded by 14n is obtained for n-bit binary addmon. Expand
...
1
2
...