On the Single-Source Unsplittable Flow Problem

Let G=(V, E) be a capacitated directed graph with a source s and k terminals t/sub i/ with demands d/sub i/, 1/spl les/i/spl les/k. We would like to concurrently route every demand on a single path from s to the corresponding terminal without violating the capacities. There are several interesting and important variations of this unsplittable flow problem. If the necessary cut condition is satisfied, we show how to compute an unsplittable flow satisfying the demands such that the total flow through any edge exceeds its capacity by at most the maximum demand. For graphs in which all capacities are at least the maximum demand, we therefore obtain an unsplittable flow with congestion at most 2, and this result is best possible. Furthermore, we show that all demands can be routed unsplittable in 5 rounds, i. e. , all demands can be collectively satisfied by the union of 5 unsplittable flows. Finally, we show that 22. 6% of the total demand can be satisfied unsplittably. These results are extended to the case when the cut condition is not necessarily satisfied. We derive a 2-approximation algorithm for congestion, a 5-approximation algorithm for the number of rounds and a 4. 43=1/0. 226-approximation algorithm for the maximum routable demand.

Authors

• Yefim Dinitz
• Naveen Garg 0001
• Michel X. Goemans

Keywords

• Computer science
• Read only memory
• Contracts
• Routing
• Flow Problem
• Unsplittable Flow
• Total Flow
• Total Demand
• Single Path
• Maximum Demand
• Less Than Or Equal
• Maximum Flow
• Version Of Problem
• Minimum Flow
• Fractional Flow
• Single Edge
• Makespan
• Parallel Machines
• Net Inflows
• Incoming Edges
• Outgoing Edges
• Previous Lemma
• Special Case Of Problem
• Bin Packing
• Original Capacity
• Job Processing Times
• Minimum Cost Flow