Single-Source Unsplittable Flow

The max-flow min-cut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity Menger's theorem provides a good characterization for the following single-source disjoint paths problem: given a graph G, with a source vertex s and terminals t/sub 1/, .. ., t/sub k/, decide whether there exist edge-disjoint s-t/sub i/ paths for i=1, .. ., k. We consider a natural, NP-hard generalization of this problem, which we call the single-source unsplittable flow problem. We are given a source and terminals as before; but now each terminal t/sub i/ has a demand p/sub i//spl les/1, and each edge e of G has a capacity c/sub e//spl ges/1. The problem is to decide whether one can choose a single s-t/sub i/ path for each i, so that the resulting set of paths respects the capacity constraints-the total amount of demand routed across any edge e must be bounded by the capacity c/sub e/. The main results of this paper are constant-factor approximation algorithms for three natural optimization versions of this problem, in arbitrary directed and undirected graphs. The development of these algorithms requires a number of new techniques for rounding fractional solutions to network flow problems; for two of the three problems we consider, there were no previous techniques capable of providing an approximation in the general case, and for the third, the randomized rounding algorithm of Raghavan and Thompson provides a logarithmic approximation. Our techniques are also of interest from the perspective of a family of NP-hard load balancing and machine scheduling problems that can be reduced to the single-source unsplittable flow problem.

Authors

• Jon M. Kleinberg

Keywords

• Routing
• Approximation algorithms
• Computer science
• Constraint optimization
• Load management
• Processor scheduling
• Admission control
• Scheduling algorithm
• Postal services
• Graph theory
• Unsplittable Flow
• General Case
• Estimation Algorithm
• Flow Problem
• Load Balancing
• Version Of Problem
• Amount Of Demand
• Machine Scheduling Problem
• Source Vertex
• Central Node
• Directed Graph
• Version Of The Paper
• Maximum Flow
• Flow Path
• Total Demand
• Basic Problem
• General Flow
• Polynomial-time Algorithm
• Approximate Ratio
• Fractional Flow
• Arbitrary Graph
• Part Of Path
• Terminal Pair
• Flow Units
• Maximum Demand
• Minimum Cost Flow
• Flow Algorithm
• Network Routing
• Depth-first
• Amount Of Flow