Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Meet and merge: approximation algorithms for confluent flows
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Improved Approximation Algorithms for Unsplittable Flow Problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Single-source unsplittable flow
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
(Almost) tight bounds and existence theorems for confluent flows
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Optimizing OSPF/IS-IS weights in a changing world
IEEE Journal on Selected Areas in Communications
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A d-furcated flow is a network flow whose support graph has maximum out degree d. Take a single-sink multi-commodity flow problem on any network and with any set of routing demands. Then we show that the existence of feasible fractional flow with node congestion one implies the existence of a d-furcated flow with congestion at most 1+1/(d-1), for d ≥ 2. This result is tight, and sothe congestion gap for d-furcated flows is bounded andexactly equal to 1+ 1/(d-1). For the case d=1 (confluent flows), it is known that the congestion gap is unbounded, namely Θ(log n). Thus, allowing single-sink multicommodity network flows to increase their maximum out degree from one to two virtually eliminates this previously observed congestion gap. As a corollary we obtain a factor 1 + 1/(d-1)-approximation algorithm for the problem of finding a minimum congestion d-furcated flow; we also prove that this problem is max SNP-hard. Using known techniques these results also extend to degree-constrained unsplittable routing,where each individual demand must be routed along a unique path.