Faster and simpler approximation algorithms for mixed packing and covering problems
نویسندگان
چکیده
منابع مشابه
Faster and simpler approximation algorithms for mixed packing and covering problems
We propose an algorithm for approximately solving the mixed packing and covering problem; given a convex compact set ∅ = B ⊆ RN , either compute x ∈ B such that f (x) ≤ (1 + )a and g(x) ≥ (1 − )b or decide that {x ∈ B | f (x) ≤ a, g(x) ≥ b} = ∅. Here f, g : B → RM + are vectors whose components are M non-negative convex and concave functions, respectively, and a, b ∈ RM ++ are constant positive...
متن کاملFaster approximation algorithms for packing and covering problems∗
We adapt a method proposed by Nesterov [19] to design an algorithm that computes optimal solutions to fractional packing problems by solving O∗( −1 √ Kn) separable convex quadratic programs, where K is the maximum number of non-zeros per row and n is the number of variables. We also show that the quadratic program can be approximated to any degree of accuracy by an appropriately defined piecewi...
متن کاملApproximation Algorithms for Mixed Fractional Packing and Covering Problems
We propose an approximation algorithm based on the Lagrangian or price directive decomposition method to compute an -approximate solution of the mixed fractional packing and covering problem: find x 2 B such that f(x) (1 + )a, g(x) (1 )b where f(x); g(x) are vectors with M nonnegative convex and concave functions, a and b are M dimensional nonnegative vectors and B is a convex set that can be q...
متن کاملApproximation Algorithms for Covering and Packing Problems on Paths
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances, which are fast and yet come close to the optimal value. In this thesis, we study the design and analysis of approximation algorithms for such problems. We f...
متن کاملFast Approximation Algorithms for Fractional Packing and Covering Problems
Thii paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniiues. The techniques developed in this paper greatly outperform the general methods in many applications, and are extensions of a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2007
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2007.02.064