Paper Info
Title
Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time
Abstract
For the vast majority of local problems on graphs of small tree width (where by local we mean that a solution can be verified by checking separately the neighbourhood of each vertex), standard dynamic programming techniques give c^tw |V|^O(1) time algorithms, where tw is the tree width of the input graph G = (V, E) and c is a constant. On the other hand, for problems with a global requirement (usually connectivity) the best -- known algorithms were naive dynamic programming schemes running in at least tw^tw time. We breach this gap by introducing a technique we named Cut&Count that allows to produce c^tw |V|^O(1) time Monte Carlo algorithms for most connectivity-type problems, including Hamiltonian Path, Steiner Tree, Feedback Vertex Set and Connected Dominating Set. These results have numerous consequences in various fields, like parameterized complexity, exact and approximate algorithms on planar and H-minor-free graphs and exact algorithms on graphs of bounded degree. The constant c in our algorithms is in all cases small, and in several cases we are able to show that improving those constants would cause the Strong Exponential Time Hypothesis to fail. In contrast to the problems aiming to minimize the number of connected components that we solve using Cut&Count as mentioned above, we show that, assuming the Exponential Time Hypothesis, the aforementioned gap cannot be breached for some problems that aim to maximize the number of connected components like Cycle Packing.
Year
DOI
Venue
2011
10.1109/FOCS.2011.23
foundations of computer science
Keywords
DocType
Volume
constant c,tw time,time monte carlo algorithm,aforementioned gap,connected dominating set,single exponential time,exponential time hypothesis,connected component,time algorithm,feedback vertex set,strong exponential time hypothesis,dynamic programming,approximation theory,monte carlo methods,steiner trees,set theory,treewidth,polynomials,randomized algorithms,approximation algorithms,computational complexity
Conference
abs/1103.0534
ISSN
Citations 
PageRank 
0272-5428
48
1.28
References 
Authors
0
6
Name
Order
Citations
PageRank
Marek Cygan155640.52
Jesper Nederlof229424.22
Marcin Pilipczuk343647.86
michal pilipczuk440351.93
Joham M. M. van Rooij5481.28
jakub onufry wojtaszczyk61549.48