---
_id: '476'
abstract:
- lang: eng
text: 'An elementary h-route ow, for an integer h 1, is a set of h edge- disjoint
paths between a source and a sink, each path carrying a unit of ow, and an h-route
ow is a non-negative linear combination of elementary h-routeows. An h-route cut
is a set of edges whose removal decreases the maximum h-route ow between a given
source-sink pair (or between every source-sink pair in the multicommodity setting)
to zero. The main result of this paper is an approximate duality theorem for multicommodity
h-route cuts and ows, for h 3: The size of a minimum h-route cut is at least f=h
and at most O(log4 k f) where f is the size of the maximum h-routeow and k is
the number of commodities. The main step towards the proof of this duality is
the design and analysis of a polynomial-time approximation algorithm for the minimum
h-route cut problem for h = 3 that has an approximation ratio of O(log4 k). Previously,
polylogarithmic approximation was known only for h-route cuts for h 2. A key ingredient
of our algorithm is a novel rounding technique that we call multilevel ball-growing.
Though the proof of the duality relies on this algorithm, it is not a straightforward
corollary of it as in the case of classical multicommodity ows and cuts. Similar
results are shown also for the sparsest multiroute cut problem.'
author:
- first_name: Petr
full_name: Kolman, Petr
last_name: Kolman
- first_name: Christian
full_name: Scheideler, Christian
id: '20792'
last_name: Scheideler
citation:
ama: 'Kolman P, Scheideler C. Towards Duality of Multicommodity Multiroute Cuts
and Flows: Multilevel Ball-Growing. *Theory of Computing Systems*. 2013;(2):341-363.
doi:10.1007/s00224-013-9454-3'
apa: 'Kolman, P., & Scheideler, C. (2013). Towards Duality of Multicommodity
Multiroute Cuts and Flows: Multilevel Ball-Growing. *Theory of Computing Systems*,
(2), 341–363. https://doi.org/10.1007/s00224-013-9454-3'
bibtex: '@article{Kolman_Scheideler_2013, title={Towards Duality of Multicommodity
Multiroute Cuts and Flows: Multilevel Ball-Growing}, DOI={10.1007/s00224-013-9454-3},
number={2}, journal={Theory of Computing Systems}, publisher={Springer}, author={Kolman,
Petr and Scheideler, Christian}, year={2013}, pages={341–363} }'
chicago: 'Kolman, Petr, and Christian Scheideler. “Towards Duality of Multicommodity
Multiroute Cuts and Flows: Multilevel Ball-Growing.” *Theory of Computing Systems*,
no. 2 (2013): 341–63. https://doi.org/10.1007/s00224-013-9454-3.'
ieee: 'P. Kolman and C. Scheideler, “Towards Duality of Multicommodity Multiroute
Cuts and Flows: Multilevel Ball-Growing,” *Theory of Computing Systems*,
no. 2, pp. 341–363, 2013.'
mla: 'Kolman, Petr, and Christian Scheideler. “Towards Duality of Multicommodity
Multiroute Cuts and Flows: Multilevel Ball-Growing.” *Theory of Computing Systems*,
no. 2, Springer, 2013, pp. 341–63, doi:10.1007/s00224-013-9454-3.'
short: P. Kolman, C. Scheideler, Theory of Computing Systems (2013) 341–363.
date_created: 2017-10-17T12:42:24Z
date_updated: 2022-01-06T07:01:21Z
ddc:
- '040'
department:
- _id: '79'
doi: 10.1007/s00224-013-9454-3
file:
- access_level: closed
content_type: application/pdf
creator: florida
date_created: 2018-03-15T14:07:18Z
date_updated: 2018-03-15T14:07:18Z
file_id: '1326'
file_name: 476-tocsrevised3b.pdf
file_size: 264308
relation: main_file
success: 1
file_date_updated: 2018-03-15T14:07:18Z
has_accepted_license: '1'
issue: '2'
page: 341-363
project:
- _id: '1'
name: SFB 901
- _id: '5'
name: SFB 901 - Subprojekt A1
- _id: '2'
name: SFB 901 - Project Area A
publication: Theory of Computing Systems
publisher: Springer
status: public
title: 'Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing'
type: journal_article
user_id: '477'
year: '2013'
...