Distributed Algorithms for Scheduling on Line and Tree Networks with Non-uniform Bandwidths

In this paper we study the unsplittable flow problem (UFP) on tree networks in a distributed setting. We have a set of processors (or agents) and a set of tree networks defined over some vertex set. Each processor can access a subset of the tree networks. Each edge in each of the tree networks is associated with a capacity. Each processor has a demand specified as a pair of vertices u and v, along with a profit and a height; the processor wishes to send data between u and v and requires bandwidth equal to its height. Towards that goal, the processor needs to select a tree network accessible to it. A feasible solution selects a subset of demands and schedules each selected demand on a tree network accessible to the processor owning the demand. The requirement is that for any tree network and any edge in the network, the sum of heights of demands scheduled on the network and passing through the edge must not exceed the capacity offered by the edge. The goal is to output a solution having the maximum aggregate profit. Prior work has addressed the above problem in a distributed setting for the special case where all the edge capacities are uniform, say one unit. The main contributions of this paper is to address the general case where the edge capacities can be non-uniform and arbitrary. For this case, we present distributed algorithms with poly-logarithmic approximation ratio.

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

[2]  Alessandro Panconesi,et al.  Fast distributed scheduling via primal-dual , 2008, SPAA '08.

[3]  Stavros G. Kolliopoulos.  Edge-Disjoint Paths and Unsplittable Flow , 2007, Handbook of Approximation Algorithms and Metaheuristics.

[4]  Nikhil Bansal,et al.  A logarithmic approximation for unsplittable flow on line graphs , 2014, TALG.

[5]  Baruch Schieber,et al.  A quasi-PTAS for unsplittable flow on line graphs , 2006, STOC '06.

[6]  Yogish Sabharwal,et al.  Distributed Algorithms for Scheduling on Line and Tree Networks with Non-uniform Bandwidths , 2013, 2013 IEEE 27th International Symposium on Parallel and Distributed Processing.

[7]  Aravind Srinivasan,et al.  On the Complexity of Distributed Network Decomposition , 1996, J. Algorithms.

[8]  Chandra Chekuri,et al.  Unsplittable Flow in Paths and Trees and Column-Restricted Packing Integer Programs , 2009, APPROX-RANDOM.

[9]  Alessandro Panconesi,et al.  Fast primal-dual distributed algorithms for scheduling and matching problems , 2010, Distributed Computing.

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

[11]  Reuven Bar-Yehuda,et al.  A unified approach to approximating resource allocation and scheduling , 2001, JACM.

[12]  Joseph Naor,et al.  Admission Control in Networks with Advance Reservations , 2004, Algorithmica.

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

[14]  Yuval Rabani,et al.  Improved Approximation Algorithms for Resource Allocation , 2002, IPCO.

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

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

[17]  Robert E. Tarjan,et al.  Decomposition by clique separators , 1985, Discret. Math..

[18]  Michael Luby.  A Simple Parallel Algorithm for the Maximal Independent Set Problem , 1986, SIAM J. Comput..

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