Approximation Algorithms for the Unsplittable Flow Problem on Paths and Trees

We study the Unsplittable Flow Problem (UFP) and related variants, namely UFP with Bag Constraints and UFP with Rounds, on paths and trees. We provide improved constant factor approximation algorithms for all these problems under the no bottleneck assumption (NBA), which says that the maximum demand for any source-sink pair is at most the minimum capacity of any edge. We obtain these improved results by expressing a feasible solution to a natural LP relaxation of the UFP as a near-convex combination of feasible integral solutions.

[1]  Julia Chuzhoy,et al.  Resource Minimization Job Scheduling , 2009, APPROX-RANDOM.

[2]  Paul S. Bonsma,et al.  A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths , 2011, FOCS.

[3]  Sudipto Guha,et al.  Approximating the throughput of multiple machines under real-time scheduling , 1999, STOC '99.

[4]  Anamitra R. Choudhury,et al.  A Near-linear Time Constant Factor Algorithm for Unsplittable Flow Problem on Line with Bag Constraints , 2010, FSTTCS.

[5]  Yogish Sabharwal,et al.  Varying bandwidth resource allocation problem with bag constraints , 2010, 2010 IEEE International Symposium on Parallel & Distributed Processing (IPDPS).

[6]  Amit Kumar,et al.  Approximation Algorithms for the Unsplittable Flow Problem , 2002, Algorithmica.

[7]  Jun Qin,et al.  Coloring interval graphs with first-fit , 1995, Discret. Math..

[8]  Rafail Ostrovsky,et al.  Approximation algorithms for the job interval selection problem and related scheduling problems , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[9]  Piotr Berman,et al.  Improvements in throughout maximization for real-time scheduling , 2000, STOC '00.

[10]  Aris Pagourtzis,et al.  Routing and Path Multi-Coloring , 2001, Inf. Process. Lett..

[11]  Thomas Erlebach,et al.  Online Capacitated Interval Coloring , 2007, ESCAPE.

[12]  H. A. Kierstead,et al.  The Linearity of First-Fit Coloring of Interval Graphs , 1988, SIAM J. Discret. Math..

[13]  Rajiv Raman,et al.  Max-coloring and online coloring with bandwidths on interval graphs , 2011, TALG.

[14]  Chandra Chekuri,et al.  Multicommodity demand flow in a tree and packing integer programs , 2007, TALG.

[15]  Frits C. R. Spieksma,et al.  Interval selection: applications, algorithms and lower bounds , 2002 .