Routing under Balance release_nwonzg3sgvaavh5ob3rb4nhvdu

by Alina Ene, Gary Miller, Jakub Pachocki, Aaron Sidford

Released as a article .

2016  

Abstract

We introduce the notion of balance for directed graphs: a weighted directed graph is α-balanced if for every cut S ⊆ V, the total weight of edges going from S to V∖ S is within factor α of the total weight of edges going from V∖ S to S. Several important families of graphs are nearly balanced, in particular, Eulerian graphs (with α = 1) and residual graphs of (1+ϵ)-approximate undirected maximum flows (with α=O(1/ϵ)). We use the notion of balance to give a more fine-grained understanding of several well-studied routing questions that are considerably harder in directed graphs. We first revisit oblivious routings in directed graphs. Our main algorithmic result is an oblivious routing scheme for single-source instances that achieve an O(α·^3 n / n) competitive ratio. In the process, we make several technical contributions which may be of independent interest. In particular, we give an efficient algorithm for computing low-radius decompositions of directed graphs parameterized by balance. We also define and construct low-stretch arborescences, a generalization of low-stretch spanning trees to directed graphs. On the negative side, we present new lower bounds for oblivious routing problems on directed graphs. We show that the competitive ratio of oblivious routing algorithms for directed graphs is Ω(n) in general; this result improves upon the long-standing best known lower bound of Ω(√(n)) given by Hajiaghayi, Kleinberg, Leighton and Räcke in 2006. We also show that our restriction to single-source instances is necessary by showing an Ω(√(n)) lower bound for multiple-source oblivious routing in Eulerian graphs. We also give a fast algorithm for the maximum flow problem in balanced directed graphs.
In text/plain format

Archived Files and Locations

application/pdf  336.0 kB
file_ihh2isqctremnjm2ddeexyw3se
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2016-03-30
Version   v1
Language   en ?
arXiv  1603.09009v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: bd71d649-3e4d-4839-a34d-118aded27383
API URL: JSON