Paper by Erik D. Demaine

Reference:

Erik D. Demaine, MohammadTaghi Hajiaghayi, and Bojan Mohar, “Approximation Algorithms via Contraction Decomposition”, Combinatorica, volume 30, number 5, 2010, pages 533–552.

BibTeX

@Article{ContractionTSP_Combinatorica,
  AUTHOR        = {Erik D. Demaine and MohammadTaghi Hajiaghayi and
                   Bojan Mohar},
  TITLE         = {Approximation Algorithms via Contraction Decomposition},
  JOURNAL       = {Combinatorica},
  journalurl    = {http://www.springerlink.com/content/1439-6912/},
  VOLUME        = 30,
  NUMBER        = 5,
  YEAR          = 2010,
  PAGES         = {533--552},

  length        = {15 pages},
  papers        = {ContractionTSP_SODA2007},
  replaces      = {ContractionTSP_SODA2007},
  copyright     = {Copyright held by the authors.},
  comments      = {This paper is also available from <A HREF="https://doi.org/10.1007/s00493-010-2341-5">SpringerLink</A>.},
}

Abstract:

We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number k of pieces such that contracting any piece results in a graph of bounded treewidth (where the bound depends on k). This decomposition result parallels an analogous, simpler result for edge deletions instead of contractions, obtained in [Bak94, Epp00, DDO⁺04, DHK05], and it generalizes a similar result for “compression” (a variant of contraction) in planar graphs [Kle05] Our decomposition result is a powerful tool for obtaining PTASs for contraction-closed problems (whose optimal solution only improves under contraction), a much more general class than minor-closed problems. We prove that any contraction-closed problem satisfying just a few simple conditions has a PTAS in bounded-genus graphs. In particular, our framework yields PTASs for the weighted Traveling Salesman Problem and for minimum-weight c-edge-connected submultigraph on bounded-genus graphs, improving and generalizing previous algorithms of [GKP95, AGK⁺98, Kle05, Gri00, CGSZ04, BCGZ05]. We also highlight the only main difficulty in extending our results to general H-minor-free graphs.

Comments:

This paper is also available from SpringerLink.

Copyright:

Copyright held by the authors.

Length:

The paper is 15 pages.

Availability:

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Related papers:

ContractionTSP_SODA2007 (Approximation Algorithms via Contraction Decomposition)