Largest Chordal and Interval Subgraphs Faster Than 2 n

We prove that in an n-vertex graph, induced chordal and interval subgraphs with the maximum number of vertices can be found in time \(\mathcal{O}(2^{\lambda n})\) for some λ < 1. These are the first algorithms breaking the trivial 2 n n O(1) bound of the brute-force search for these problems.

[1]  John Michael Robson,et al.  Algorithms for Maximum Independent Sets , 1986, J. Algorithms.

[2]  Fedor V. Fomin,et al.  Finding Induced Subgraphs via Minimal Triangulations , 2009, STACS.

[3]  Michal Pilipczuk,et al.  Finding a Maximum Induced Degenerate Subgraph Faster Than 2 n , 2012, IPEC.

[4]  Saket Saurabh,et al.  Efficient Exact Algorithms through Enumerating Maximal Independent Sets and Other Techniques , 2007, Theory of Computing Systems.

[5]  Fedor V. Fomin,et al.  Exact Algorithm for the Maximum Induced Planar Subgraph Problem , 2011, ESA.

[6]  Fedor V. Fomin,et al.  Exact exponential algorithms , 2013, CACM.

[7]  Dieter Kratsch,et al.  On Independent Sets and Bicliques in Graphs , 2008, Algorithmica.

[8]  John M. Lewis,et al.  The Node-Deletion Problem for Hereditary Properties is NP-Complete , 1980, J. Comput. Syst. Sci..

[9]  Serge Gaspers,et al.  Exponential Time Algorithms - Structures, Measures, and Bounds , 2010 .

[10]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[11]  C. Lekkeikerker,et al.  Representation of a finite graph by a set of intervals on the real line , 1962 .

[12]  P. Seymour,et al.  The Strong Perfect Graph Theorem , 2002, math/0212070.

[13]  Saket Saurabh,et al.  Maximum r-Regular Induced Subgraph Problem: Fast Exponential Algorithms and Combinatorial Bounds , 2012, SIAM J. Discret. Math..

[14]  Fedor V. Fomin,et al.  Treewidth computation and extremal combinatorics , 2012 .

[15]  Fedor V. Fomin,et al.  On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms , 2008, Algorithmica.

[16]  Adi Shamir,et al.  A T=O(2n/2), S=O(2n/4) Algorithm for Certain NP-Complete Problems , 1981, SIAM J. Comput..

[17]  Fedor V. Fomin,et al.  Iterative Compression and Exact Algorithms , 2008, MFCS.