A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Decision algorithms for unsplittable flow and the half-disjoint paths problem
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Understanding TCP Vegas: a duality model
Journal of the ACM (JACM)
Introduction to Linear Optimization
Introduction to Linear Optimization
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Single-source unsplittable flow
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A duality model of TCP and queue management algorithms
IEEE/ACM Transactions on Networking (TON)
Cross-layer optimization in TCP/IP networks
IEEE/ACM Transactions on Networking (TON)
FAST TCP: motivation, architecture, algorithms, performance
IEEE/ACM Transactions on Networking (TON)
A logarithmic approximation for unsplittable flow on line graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Optimal and distributed protocols for cross-layer design of physical and transport layers in MANETs
IEEE/ACM Transactions on Networking (TON)
A unified approach to congestion control and node-based multipath routing
IEEE/ACM Transactions on Networking (TON)
How bad is single-path routing
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
On the approximability of the minimum congestion unsplittable shortest path routing problem
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Toward internet-wide multipath routing
IEEE Network: The Magazine of Global Internetworking
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This paper studies the performance difference of joint routing and congestion control when either single-path routes or multipath routes are used. Our performance metric is the total utility achieved by jointly optimizing transmission rates using congestion control and paths using source routing. In general, this performance difference is strictly positive and hard to determine--in fact an NP-hard problem. To better estimate this performance gap, we develop analytical bounds to this "cost of not splitting" in routing. We prove that the number of paths needed for optimal multipath routing differs from that of optimal single-path routing by no more than the number of links in the network. We provide a general bound on the performance loss, which is independent of the number of source-destination pairs when the latter is larger than the number of links in a network. We also propose a vertex projection method and combine it with a greedy branch-and-bound algorithm to provide progressively tighter bounds on the performance loss. Numerical examples are used to show the effectiveness of our approximation technique and estimation algorithms.