Abstract
Congestion minimization is a wellknown routing problem for which
there is an O(log n/loglog n)approximation via randomized rounding due to Raghavan and Thompson. Srinivasan formally introduced the lowcongestion multipath routing problem as a generalization of the (singlepath) congestion minimization problem. The goal is to route multiple disjoint paths for each pair, for the sake of fault tolerance. Srinivasan developed a dependent randomized scheme for a special case of the multipath problem when the input consists of a given set of disjoint paths for each pair and the goal is to select a given subset of them. Subsequently Doerr gave a different dependentrounding scheme and derandomization. Doerr et al. considered the problem where the paths have to be chosen, and applied the dependent rounding technique and evaluated it experimentally. However, their algorithm does not maintain the required disjointness property without which the problem easily reduces to the standard congestion minimization problem.
In this note we show a simple algorithm that solves the problem
correctly without the need for dependent rounding  standard
independent rounding suffices. This is made possible via the notion
of multiroute flows originally suggested by Kishimoto et al. One advantage of the simpler rounding is an improved bound on the congestion when the path lengths are short.
BibTeX  Entry
@InProceedings{chekuri_et_al:OASIcs:2018:8298,
author = {Chandra Chekuri and Mark Idleman},
title = {{Congestion Minimization for Multipath Routing via Multiroute Flows}},
booktitle = {1st Symposium on Simplicity in Algorithms (SOSA 2018)},
pages = {3:13:12},
series = {OpenAccess Series in Informatics (OASIcs)},
ISBN = {9783959770644},
ISSN = {21906807},
year = {2018},
volume = {61},
editor = {Raimund Seidel},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8298},
URN = {urn:nbn:de:0030drops82984},
doi = {10.4230/OASIcs.SOSA.2018.3},
annote = {Keywords: multipath routing, congestion minimization, multiroute flows}
}
Keywords: 

multipath routing, congestion minimization, multiroute flows 
Collection: 

1st Symposium on Simplicity in Algorithms (SOSA 2018) 
Issue Date: 

2018 
Date of publication: 

05.01.2018 