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Parameterized optimization in uncertain graphs-A survey and some results
Date Issued
01-01-2020
Author(s)
Indian Institute of Technology, Madras
Vijayaragunathan, R.
Abstract
We present a detailed survey of results and two new results on graphical models of uncertainty and associated optimization problems. We focus on two well-studied models, namely, the Random Failure (RF) model and the Linear Reliability Ordering (LRO) model. We present an FPT algorithm parameterized by the product of treewidth and max-degree for maximizing expected coverage in an uncertain graph under the RF model. We then consider the problem of finding the maximal core in a graph, which is known to be polynomial time solvable. We show that the PROBABILISTIC-CORE problem is polynomial time solvable in uncertain graphs under the LRO model. On the other hand, under the RF model, we show that the PROBABILISTIC-CORE problem is W[1]-hard for the parameter d, where d is the minimum degree of the core. We then design an FPT algorithm for the parameter treewidth.
Volume
13