Approximating covering integer programs with multiplicity constraints
Discrete Applied Mathematics
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Minimum-cost single-source 2-splittable flow
Information Processing Letters
Approximating the k-multicut problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Implementing approximation algorithms for the single-source unsplittable flow problem
Journal of Experimental Algorithmics (JEA)
Computer Networks: The International Journal of Computer and Telecommunications Networking
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
Theoretical Computer Science
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG)
Single source multiroute flows and cuts on uniform capacity networks
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The Influence of Link Restrictions on (Random) Selfish Routing
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Minimum-cost single-source 2-splittable flow
Information Processing Letters
Multicommodity demand flow in a tree
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Convex combinations of single source unsplittable flows
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Parameterized Tractability of Edge-Disjoint Paths on Directed Acyclic Graphs
SIAM Journal on Discrete Mathematics
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Single-source stochastic routing
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Maximizing throughput in queueing networks with limited flexibility
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
On column-restricted and priority covering integer programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Single-source k-splittable min-cost flows
Operations Research Letters
Managing the network with Merlin
Proceedings of the Twelfth ACM Workshop on Hot Topics in Networks
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In the single-source unsplittable flow problem, we are given a network G, a source vertex s, and k commodities with sinks ti and real-valued demands $\rho_i,$ $1\leq i \leq k.$ We seek to route the demand $\rho_i$ of each commodity i along a single s-ti flow path so that the total flow routed across any edge e is bounded by the edge capacity ue. The conceptual difficulty of this NP-hard problem arises from combining packing constraints due to the existence of capacities with path selection in a graph of arbitrary topology. In this paper we give a generic framework, which yields approximation algorithms that are simpler than those previously known and achieve significant improvements upon the approximation ratios. Our framework, with appropriate subroutines, applies to all optimization versions previously considered and, unlike previous work, treats in a unified manner directed and undirected graphs. We provide extensions of our algorithms which yield the best possible approximation guarantees for restricted sets of demand values and an associated scheduling problem.