On Listing, Sampling, and Counting the Chordal Graphs with Edge Constraints
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Approximating the Minimum Chain Completion problem
Information Processing Letters
Characterizing minimal interval completions towards better understanding of profile and pathwidth
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On listing, sampling, and counting the chordal graphs with edge constraints
Theoretical Computer Science
Approximation algorithms for minimum chain vertex deletion
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Subexponential parameterized algorithm for minimum fill-in
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A parameterized algorithm for chordal sandwich
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
| Hi-index | 0.00 |
In the minimum fill-in problem, one wishes to find a set of edges of smallest size, whose addition to a given graph will make it chordal. The problem has important applications in numerical algebra and has been studied intensively since the 1970s. We give the first polynomial approximation algorithm for the problem. Our algorithm constructs a triangulation whose size is at most eight times the optimum size squared. The algorithm builds on the recent parameterized algorithm of Kaplan, Shamir, and Tarjan for the same problem.For bounded degree graphs we give a polynomial approximation algorithm with a polylogarithmic approximation ratio. We also improve the parameterized algorithm.