Computer Science – Data Structures and Algorithms
Scientific paper
2011-03-02
Computer Science
Data Structures and Algorithms
89 pages, 12 figures
Scientific paper
For the vast majority of local graph problems standard dynamic programming techniques give c^tw V^O(1) algorithms, where tw is the treewidth of the input graph. On the other hand, for problems with a global requirement (usually connectivity) the best-known algorithms were naive dynamic programming schemes running in tw^O(tw) V^O(1) time. We breach this gap by introducing a technique we dubbed Cut&Count that allows to produce c^tw V^O(1) Monte Carlo algorithms for most connectivity-type problems, including Hamiltonian Path, Feedback Vertex Set and Connected Dominating Set, consequently answering the question raised by Lokshtanov, Marx and Saurabh [SODA'11] in a surprising way. We also show that (under reasonable complexity assumptions) the gap cannot be breached for some problems for which Cut&Count does not work, like CYCLE PACKING. The constant c we obtain is in all cases small (at most 4 for undirected problems and at most 6 for directed ones), and in several cases we are able to show that improving those constants would cause the Strong Exponential Time Hypothesis to fail. Our results have numerous consequences in various fields, like FPT algorithms, exact and approximate algorithms on planar and H-minor-free graphs and algorithms on graphs of bounded degree. In all these fields we are able to improve the best-known results for some problems.
Cygan Marek
Nederlof Jesper
Pilipczuk Marcin
Pilipczuk Michał
Rooij Johan van
No associations
LandOfFree
Solving connectivity problems parameterized by treewidth in single exponential 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 Solving connectivity problems parameterized by treewidth in single exponential time, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Solving connectivity problems parameterized by treewidth in single exponential time will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-587916