Advertisement

Algorithmica

, Volume 36, Issue 2, pp 179–205 | Cite as

A New Approximation Algorithm for Finding Heavy Planar Subgraphs

  • Călinescu
  • Fernandes
  • Karloff
  • Zelikovsky
Article

Abstract

We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NP-hard problem of finding a heaviest planar subgraph in an edge-weighted graph G . This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH had a performance ratio exceeding 1/3 , which is obtained by any algorithm that produces a maximum weight spanning tree in G . Based on the Berman—Ramaiyer Steiner tree algorithm, the new algorithm has performance ratio at least 1/3+1/72 and at most 5/12 . We also show that if G is complete and its edge weights satisfy the triangle inequality, then the performance ratio is at least 3/8 . Furthermore, we derive the first nontrivial performance ratio (7/12 instead of 1/2 ) for the NP-hard SC MAXIMUM WEIGHT OUTERPLANAR SUBGRAPH problem.

Keywords

Weighted planar graph Approximation algorithm Performance ratio 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 2003

Authors and Affiliations

  • Călinescu
    • 1
  • Fernandes
    • 2
  • Karloff
    • 3
  • Zelikovsky
    • 4
  1. 1.Department of Computer ScienceIllinois Institute of TechnologyChicagoUSA
  2. 2.Department of Computer ScienceUniversity of São PauloSao PauloBrazil
  3. 3.AT&T Laboratories—Research, Room C231Florham ParkUSA
  4. 4.Department of Computer ScienceGeorgia State UniversityAtlantaUSA

Personalised recommendations