Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Global Minimum Cuts in Surface-Embedded Graphs

  • Erin W. Chambers
  • Jeff Erickson
  • Kyle Fox
  • Amir Nayyeri
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_683-1

Years and Authors of Summarized Original Work

2009; Chambers, Erickson, Nayyeri

2011; Erickson, Nayyeri

2012; Erickson, Fox, Nayyeri

Problem Definition

Given a graph G in which every edge has a nonnegative capacity, the goal of the minimum-cut problem is to find a subset of edges of G with minimum total capacity whose deletion disconnects G. The closely related minimum (s, t)-cut problem further requires two specific vertices s and t to be separated by the deleted edges. Minimum cuts and their generalizations play a central role in divide-and-conquer and network optimization algorithms.

The fastest algorithms known for computing minimum cuts in arbitrary graphs run in roughly O(mn) time for graphs with n vertices and medges. However, even faster algorithms are known for graphs with additional topological structure. This entry sketches algorithms to compute minimum cuts in near-linear time when the input graph can be drawn on a surface with bounded genus – informally, a sphere with a...

Keywords

Topological graph theory Graph embedding Minimum cuts Homology Covering spaces Fixed-parameter tractability 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Erin W. Chambers
    • 1
  • Jeff Erickson
    • 2
  • Kyle Fox
    • 3
  • Amir Nayyeri
    • 4
  1. 1.Department of Computer Science and MathematicsSaint Louis UniversitySt. Louis, MOUSA
  2. 2.Department of Computer ScienceUniversity of IllinoisUrbana, ILUSA
  3. 3.Institute for Computational and Experimental Research in MathematicsBrown UniversityProvidence, RIUSA
  4. 4.Department of Electrical Engineering and Computer ScienceOregon State UniversityCorvallis, ORUSA