Abstract
We consider the stochastic unsplittable flow problem: given a graph with edgecapacities, and sourcesink pairs with each pair having a size and a value, the goal is to route the pairs unsplittably while respecting edge capacities to maximize the total value of the routed pairs. However, the size of each pair is a random variable and is revealed only after we decide to route that pair. Which pairs should we route, along which paths, and in what order so as to maximize the expected value?
We present results for several cases of the problem under the nobottleneck assumption. We show a logarithmic approximation algorithm for the singlesink problem on general graphs, considerably improving on the prior results of Chawla and Roughgarden which worked for planar graphs. We present an approximation to the stochastic unsplittable flow problem on directed acyclic graphs, within less than a logarithmic factor of the best known approximation in the nonstochastic setting. We present a nonadaptive strategy on trees that is within a constant factor of the best adaptive strategy, asymptotically matching the best results for the nonstochastic unsplittable flow problem on trees. Finally, we give results for the stochastic unsplittable flow problem on general graphs.
Our techniques include using edgeconfluent flows for the singlesink problem in order to control the interaction between flowpaths, and a reduction from general scheduling policies to "safe" ones (i.e., those guaranteeing no capacity violations), which may be of broader interest.
BibTeX  Entry
@InProceedings{gupta_et_al:LIPIcs:2017:7556,
author = {Anupam Gupta and Archit Karandikar},
title = {{Stochastic Unsplittable Flows}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
pages = {7:17:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770446},
ISSN = {18688969},
year = {2017},
volume = {81},
editor = {Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7556},
URN = {urn:nbn:de:0030drops75569},
doi = {10.4230/LIPIcs.APPROXRANDOM.2017.7},
annote = {Keywords: Approximation Algorithms, Stochastic optimization, confluent flows, unsplittable flows}
}
Keywords: 

Approximation Algorithms, Stochastic optimization, confluent flows, unsplittable flows 
Collection: 

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017) 
Issue Date: 

2017 
Date of publication: 

11.08.2017 