Computer Science – Data Structures and Algorithms
Scientific paper
2011-04-12
Computer Science
Data Structures and Algorithms
Full version
Scientific paper
Many algorithms have been developed for NP-hard problems on graphs with small treewidth k. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth. It turns out that the bottleneck of many algorithms for NP-hard problems is the computation of a tree decomposition of width O(k). In particular, by the bidimensional theory, there are many linear extended monadic second order problems that can be solved on n-vertex planar graphs with treewidth k in a time linear in n and subexponential in k if a tree decomposition of width O(k) can be found in such a time. We present the first algorithm that, on n-vertex planar graphs with treewidth k, finds a tree decomposition of width O(k) in such a time. In more detail, our algorithm has a running time of O(n k^3 log k). The previous best algorithm with a running time subexponential in k was the algorithm of Gu and Tamaki [12] with a running time of O(n^(1+epsilon) log n) and an approximation ratio 1.5+1/epsilon for any epsilon>0. The running time of our algorithm is also better than the running time of O(f(k) n log n) of Reed's algorithm [17] for general graphs, where f is a function exponential in k.
Kammer Frank
Tholey Torsten
No associations
LandOfFree
Approximate Tree Decompositions of Planar Graphs in Linear Time does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Approximate Tree Decompositions of Planar Graphs in Linear Time, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximate Tree Decompositions of Planar Graphs in Linear Time will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-731118