Theory of linear and integer programming
Theory of linear and integer programming
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A cycle augmentation algorithm for minimum cost multicommodity flows on a ring
Discrete Applied Mathematics
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Approximation Algorithms for Single-Source Unsplittable Flow
SIAM Journal on Computing
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Improved Approximation Algorithms for Resource Allocation
Proceedings of the 9th 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
On 2-Coverings and 2-Packings of Laminar Families
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Journal of Computer and System Sciences
The all-or-nothing multicommodity flow problem
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
Edge-disjoint paths in Planar graphs with constant congestion
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
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
Throughput maximization for periodic packet routing on trees and grids
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
k-edge-connectivity: approximation and LP relaxation
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Iterative packing for demand and hypergraph matching
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Scheduling resources for throughput maximization
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Resource allocation for covering time varying demands
ESA'11 Proceedings of the 19th European conference on Algorithms
Pricing on paths: a PTAS for the highway problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On column-restricted and priority covering integer programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
On k-column sparse packing programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Routing in undirected graphs with constant congestion
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Distributed algorithms for scheduling on line and tree networks
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Topology-aware VM migration in bandwidth oversubscribed datacenter networks
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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 stochastic probing problem with applications
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)
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We consider requests for capacity in a given tree network T = (V, E) where each edge e of the tree has some integer capacity ue. Each request f is a node pair with an integer demand df and a profit wf which is obtained if the request is satisfied. The objective is to find a set of demands that can be feasibly routed in the tree and which provides a maximum profit. This generalizes well-known problems, including the knapsack and b-matching problems. When all demands are 1, we have the integer multicommodity flow problem. Garg et al. [1997] had shown that this problem is NP-hard and gave a 2-approximation algorithm for the cardinality case (all profits are 1) via a primal-dual algorithm. Our main result establishes that the integrality gap of the natural linear programming relaxation is at most 4 for the case of arbitrary profits. Our proof is based on coloring paths on trees and this has other applications for wavelength assignment in optical network routing. We then consider the problem with arbitrary demands. When the maximum demand dmax is at most the minimum edge capacity umin, we show that the integrality gap of the LP is at most 48. This result is obtained by showing that the integrality gap for the demand version of such a problem is at most 11.542 times that for the unit-demand case. We use techniques of Kolliopoulos and Stein [2004, 2001] to obtain this. We also obtain, via this method, improved algorithms for line and ring networks. Applications and connections to other combinatorial problems are discussed.