Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Edge-disjoint paths in expander graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Off-line admission control for general scheduling problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems
Mathematics of Operations Research
Approximation algorithms
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Strongly Polynomial Algorithms for the Unsplittable Flow Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximation Algorithms for the Unsplittable Flow Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The Directed Subgraph Homeomorphism Problem
The Directed Subgraph Homeomorphism Problem
Short paths in expander graphs
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Journal of Computer and System Sciences
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A quasi-PTAS for unsplittable flow on line graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Logarithmic hardness of the undirected edge-disjoint paths problem
Journal of the ACM (JACM)
Improved bounds for the unsplittable flow problem
Journal of Algorithms
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG)
A logarithmic approximation for unsplittable flow on line graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Unsplittable Flow in Paths and Trees and Column-Restricted Packing Integer Programs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
An improved approximation algorithm for resource allocation
ACM Transactions on Algorithms (TALG)
A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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We consider the unsplittable flow problem on a line. In this problem, we are given a set of n tasks, each specified by a start time si, an end time ti, a demand di 0, and a profit pi 0. A task, if accepted, requires di units of “bandwidth” from time si to ti and accrues a profit of pi. For every time t, we are also specified the available bandwidth ct, and the goal is to find a subset of tasks with maximum profit subject to the bandwidth constraints. We present the first polynomial time O(log n) approximation algorithm for this problem. This significantly advances the state of the art, as no polynomial time o(n) approximation was known previously. Previous results for this problem were known only in more restrictive settings; in particular, either the instance satisfies the so-called “no-bottleneck” assumption: maxi di ≤ mint ct, or the ratio of both maximum to minimum demands and maximum to minimum capacities are polynomially (or quasi-polynomially) bounded in n. Our result, on the other hand, does not require these assumptions. Our algorithm is based on a combination of dynamic programming and rounding a natural linear programming relaxation for the problem. While there is an Ω(n) integrality gap known for this LP relaxation, our key idea is to exploit certain structural properties of the problem to show that instances that are bad for the LP can in fact be handled using dynamic programming.