Computing Maximum C-Planar Subgraphs

نویسندگان

  • Markus Chimani
  • Carsten Gutwenger
  • Mathias Jansen
  • Karsten Klein
  • Petra Mutzel
چکیده

Deciding c-planarity for a given clustered graph C = (G, T ) is one of the most challenging problems in current graph drawing research. Though it is yet unknown if this problem is solvable in polynomial time, latest research focused on algorithmic approaches for special classes of clustered graphs. In this paper, we introduce an approach to solve the general problem using integer linear programming (ILP) techniques. We give an ILP formulation that also includes the natural generalization of cplanarity testing—the maximum c-planar subgraph problem—and solve this ILP with a branch-and-cut algorithm. Our computational results show that this approach is already successful for many clustered graphs of small to medium sizes and thus can be the foundation of a practically efficient algorithm that integrates further sophisticated ILP techniques.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Maximum Upward Planar Subgraphs of Embedded Planar Digraphs

Let G be an embedded planar digraph. A maximum upward planar subgraph of G is an embedding preserving subgraph that is upward planar and, among those, has the maximum number of edges. This paper presents an extensive study on the problem of computing maximum upward planar subgraphs of embedded planar digraphs: Complexity results, algorithms, and experiments are presented. Namely: (i) we prove t...

متن کامل

Maximum Weighted Induced Bipartite Subgraphs and Acyclic Subgraphs of Planar Cubic Graphs

We study the node-deletion problem consisting of finding a maximum weighted induced bipartite subgraph of a planar graph with maximum degree three. We show that this is polynomially solvable. It was shown in [4] that it is NP-complete if the maximum degree is four. We also extend these ideas to the problem of balancing signed graphs. We also consider maximum weighted induced acyclic subgraphs o...

متن کامل

Counting Subgraphs via Homomorphisms

We introduce a generic approach for counting subgraphs in a graph. The main idea is to relate counting subgraphs to counting graph homomorphisms. This approach provides new algorithms and unifies several well known results in algorithms and combinatorics including the recent algorithm of Björklund, Husfeldt and Koivisto for computing the chromatic polynomial, the classical algorithm of Kohn, Go...

متن کامل

Maximum Planar Subgraphs and Nice Embeddings :

In automatic graph drawing a given graph has to be layed-out in the plane, usually according to a number of topological and aesthetic constraints. Nice drawings for sparse nonplanar graphs can be achieved by determining a maximum planar subgraph and augmenting an embedding of this graph. This approach appears to be of limited value in practice, because the maximum planar subgraph problem is NP-...

متن کامل

Finding Large Planar Subgraphs and Large Subgraphs of a Given Genus

We consider the MAXIMUM PLANAR SUBGRAPH problem given a graph G, nd a largest planar subgraph of G. This problem has applications in circuit layout, facility layout, and graph drawing. We improve to 4/9 the best known approximation ratio for the MAXIMUM PLANAR SUBGRAPH problem. We also consider a generalization of the previous problem, the MAXIMUM GENUS D SUBGRAPH problem-given a connected grap...

متن کامل

Maximum Planar Subgraphs in Dense Graphs

Kühn, Osthus and Taraz showed that for each γ > 0 there exists C such that any n-vertex graph with minimum degree γn contains a planar subgraph with at least 2n−C edges. We find the optimum value of C for all γ < 1/2 and sufficiently large n.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008