The polyhedral approach to the maximum planar subgraph problem: New chances for related problems

  • Michael Jünger
  • Petra Mutzel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 894)

Abstract

In [JM94] we used a branch and cut algorithm in order to determine a maximum weight planar subgraph of a given graph. One of the motivations was to produce a nice drawing of a given graph by drawing the found maximum planar subgraph, and then augmenting this drawing by the removed edges. Our experiments indicate that drawing algorithms for planar graphs which require 2- or 3-connectivity, resp. degree-constraints, in addition to planarity often give “nicer” results. Thus we are led to the following problems:
  1. (1)

    Find a maximum planar subgraph with maximum degree d ∈ IN.

     
  2. (2)

    Augment a planar graph to a K-connected planar graph.

     
  3. (3)

    Find a maximum planar k-connected subgraph of a given k-connected graph.

     
  4. (4)

    Given a graph G, which is not necessarily planar and not necessarily k-connected, determine a new graph H by removing r edges and adding a edges such that the new graph H is planar, spanning, k-connected, each node v has degree at most D(v) and r+a is minimum.

     

Problems (1), (2) and (3) have been discussed in the literature, we argue that a solution to the newly defined problem (4) is most useful for our goal. For all four problems we give a polyhedral formulation by defining different linear objective functions over the same polytope which is the intersection of the planar subgraph polytope [JM93], the k-connected subgraph polytope [S92] and the degree-constrained subgraph polytope. We point out why we are confident that a branch and cut algorithm for the new problem will be an implementable and useful tool in automatic graph drawing.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Michael Jünger
    • 1
  • Petra Mutzel
    • 1
  1. 1.Universität zu KölnKölnGermany

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