eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-09-15
7:1
7:17
10.4230/LIPIcs.APPROX/RANDOM.2022.7
article
Local Treewidth of Random and Noisy Graphs with Applications to Stopping Contagion in Networks
Mehta, Hermish
1
Reichman, Daniel
2
Citadel Securities, Chicago, IL, USA
Department of Computer Science, Worcester Polytechnic Institute, MA, USA
We study the notion of local treewidth in sparse random graphs: the maximum treewidth over all k-vertex subgraphs of an n-vertex graph. When k is not too large, we give nearly tight bounds for this local treewidth parameter; we also derive nearly tight bounds for the local treewidth of noisy trees, trees where every non-edge is added independently with small probability. We apply our upper bounds on the local treewidth to obtain fixed parameter tractable algorithms (on random graphs and noisy trees) for edge-removal problems centered around containing a contagious process evolving over a network. In these problems, our main parameter of study is k, the number of initially "infected" vertices in the network. For the random graph models we consider and a certain range of parameters the running time of our algorithms on n-vertex graphs is 2^o(k) poly(n), improving upon the 2^Ω(k) poly(n) performance of the best-known algorithms designed for worst-case instances of these edge deletion problems.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol245-approx-random2022/LIPIcs.APPROX-RANDOM.2022.7/LIPIcs.APPROX-RANDOM.2022.7.pdf
Graph Algorithms
Random Graphs
Data Structures and Algorithms
Discrete Mathematics