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Fractional Routing on Pairs of Failure-disjoint Paths

(2014) In Discrete Applied Mathematics 164. p.47-60
Abstract
Given a set of commodities and a network where some arcs can fail while others are reliable, we consider a routing problem with respect to a survivability requirement that each commodity can be split among pairs of failure-disjoint paths. Two paths p and p′ form a pair of failure-disjoint paths if they share only reliable arcs. The same flow is sent over p and p′, but the flow sent on a common reliable arc is not doubled.

We present a compact linear formulation of the problem. Also three non-compact formulations solvable by column generation are introduced. In the first formulation, the generated columns correspond to pairs of failure-disjoint paths, while in the second formulation the generated columns correspond to... (More)
Given a set of commodities and a network where some arcs can fail while others are reliable, we consider a routing problem with respect to a survivability requirement that each commodity can be split among pairs of failure-disjoint paths. Two paths p and p′ form a pair of failure-disjoint paths if they share only reliable arcs. The same flow is sent over p and p′, but the flow sent on a common reliable arc is not doubled.

We present a compact linear formulation of the problem. Also three non-compact formulations solvable by column generation are introduced. In the first formulation, the generated columns correspond to pairs of failure-disjoint paths, while in the second formulation the generated columns correspond to simple paths. The third formulation is solved by generating pairs of arc-disjoint paths. All formulations are compared numerically. On top of that we study some generalizations and some special cases of the problem of computing a shortest pair of failure-disjoint paths. One of these generalizations is equivalent to a single-commodity capacitated network design problem. (Less)
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Discrete Applied Mathematics
volume
164
pages
47 - 60
publisher
Elsevier
external identifiers
• wos:000332427400006
• scopus:84893719261
ISSN
1872-6771
DOI
10.1016/j.dam.2011.12.019
language
English
LU publication?
yes
id
0f78be44-f7b4-4d76-af4b-4c71f4dd1688 (old id 3410295)
2016-04-01 09:53:26
date last changed
2021-09-22 04:16:04
```@article{0f78be44-f7b4-4d76-af4b-4c71f4dd1688,
abstract     = {Given a set of commodities and a network where some arcs can fail while others are reliable, we consider a routing problem with respect to a survivability requirement that each commodity can be split among pairs of failure-disjoint paths. Two paths p and p′ form a pair of failure-disjoint paths if they share only reliable arcs. The same flow is sent over p and p′, but the flow sent on a common reliable arc is not doubled.<br/><br>
<br/><br>
We present a compact linear formulation of the problem. Also three non-compact formulations solvable by column generation are introduced. In the first formulation, the generated columns correspond to pairs of failure-disjoint paths, while in the second formulation the generated columns correspond to simple paths. The third formulation is solved by generating pairs of arc-disjoint paths. All formulations are compared numerically. On top of that we study some generalizations and some special cases of the problem of computing a shortest pair of failure-disjoint paths. One of these generalizations is equivalent to a single-commodity capacitated network design problem.},
author       = {Ben-Ameur, Walid and Pioro, Michal and Zotkiewicz, Mateusz},
issn         = {1872-6771},
language     = {eng},
pages        = {47--60},
publisher    = {Elsevier},
series       = {Discrete Applied Mathematics},
title        = {Fractional Routing on Pairs of Failure-disjoint Paths},
url          = {http://dx.doi.org/10.1016/j.dam.2011.12.019},
doi          = {10.1016/j.dam.2011.12.019},
volume       = {164},
year         = {2014},
}

```