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Approximable Row-Column Routing Problems in All-Optical Mesh Networks (revisited)

Abstract : In all-optical networks, several communications can be transmitted through the same fiber link provided that they use different wavelengths. The MINIMUM ALL-OPTICAL ROUTING problem (given a list of pairs of nodes standing for as many point to point communication requests, assign to each request a route along with a wavelength so as to minimize the overall number of assigned wavelengths) has been paid a lot of attention and is known to be NP-hard. Rings, trees and meshes have thus been investigated as specific networks, but leading to just as many NP-hard problems. This paper investigates row-column routings in meshes (paths are allowed one turn only). We first show the MINIMUM LOAD ROW-COLUMN ROUTING problem to be NP-hard but 2-APX (more generally, the MINIMUM LOAD k-CHOICES ROUTING problem is NP-hard but k-APX), then that the MINIMUM ROW-COLUMN PATHS COLOURING problem is 4-APX (more generally, any d-segmentable routing of load L in a hypermesh of dimension d can be coloured with 2d(L-1)+1 colours at most). From there, we prove the MINIMUM ALL-OPTICAL ROW-COLUMN ROUTING problem to be APX.
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Contributor : Jérôme Palaysi <>
Submitted on : Monday, June 11, 2007 - 10:46:12 AM
Last modification on : Thursday, May 24, 2018 - 3:59:21 PM
Long-term archiving on: : Tuesday, September 21, 2010 - 1:04:02 PM


  • HAL Id : lirmm-00150160, version 2



Jérôme Palaysi, Olivier Cogis, Guillaume Bagan. Approximable Row-Column Routing Problems in All-Optical Mesh Networks (revisited). [Research Report] RR-07012, LIRMM. 2007. ⟨lirmm-00150160v2⟩



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