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
STOC '99 Proceedings of the thirty-first 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
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
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
Approximating the k-multicut problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Routing and wavelength assignment in multifiber WDM networks with non-uniform fiber cost
Computer Networks: The International Journal of Computer and Telecommunications Networking
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 fixed-parameter tractability result for multicommodity demand flow in trees
Information Processing Letters
Resource allocation in bounded degree trees
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Max-Weight Integral Multicommodity Flow in Spiders and High-Capacity Trees
Approximation and Online Algorithms
Complexity of wavelength assignment in optical network optimization
IEEE/ACM Transactions on Networking (TON)
Routing and wavelength assignment in multifiber WDM networks with non-uniform fiber cost
Computer Networks: The International Journal of Computer and Telecommunications Networking
Minimizing maximum fiber requirement in optical networks
Journal of Computer and System Sciences
Algorithmics in intensity-modulated radiation therapy
Algorithms and theory of computation handbook
Submodular function maximization via the multilinear relaxation and contention resolution schemes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Approximation algorithms for wavelength assignment
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Off-line admission control for advance reservations in star networks
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Approximation algorithms for edge-disjoint paths and unsplittable flow
Efficient Approximation and Online Algorithms
Shape rectangularization problems in intensity-modulated radiation therapy
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Online capacitated interval coloring
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Call control and routing in SONET rings
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
| Hi-index | 0.00 |
We consider requests for capacity in a given tree network T = (V, E) where each edge of the tree has some integer capacity ue. Each request consists of 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 provide 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, Vazirani, and Yannakakis [5] 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. In this paper we establish for the first time that the natural linear programming relaxation has a constant factor gap, a factor of 4, for the case of arbitrary profits. We then discuss the situation for 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 showing that the integrality gap for demand version of such a problem is at most 12 times that for the unit demand case. We use techniques of Kolliopoulos and Stein [8,9] to obtain this. We also obtain, via this method, improved algorithms for the line and ring networks. Applications and connections to other combinatorial problems are discussed.