STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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)
Edge-Disjoint Paths in Expander Graphs
SIAM Journal on Computing
Improved Approximation Algorithms for Resource Allocation
Proceedings of the 9th International IPCO Conference on Integer Programming and 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
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
Hardness of the undirected edge-disjoint paths problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
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)
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
How bad is single-path routing
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Resource allocation with time intervals
Theoretical Computer Science
On the complexity of interval scheduling with a resource constraint
Theoretical Computer Science
On k-column sparse packing programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Distributed algorithms for scheduling on line and tree networks
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Cost of not splitting in routing: characterization and estimation
IEEE/ACM Transactions on Networking (TON)
Constant integrality gap LP formulations of unsplittable flow on a path
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
A constant factor approximation algorithm for the storage allocation problem: extended abstract
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
A logarithmic approximation for unsplittable flow on line graphs
ACM Transactions on Algorithms (TALG)
Approximation algorithms for the ring loading problem with penalty cost
Information Processing Letters
Hi-index | 0.01 |
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. In this paper, we present the first polynomial-time O(log n)-approximation algorithm for this problem. No polynomial-time o(n)-approximation was known prior to this work. Previous results for this problem were known only in more restrictive settings, in particular, either if the given instance satisfies the so-called "no-bottleneck" assumption: maxi di ≤ mint ct, or else if the ratio of the maximum to the minimum demands and ratio of the maximum to the minimum capacities are polynomially (or quasi-polynomially) bounded in n. Our result, on the other hand, does not require any of 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.