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Parameterized Optimization in Uncertain Graphs—A Survey and Some Results

Department of Computer Science and Engineering, Indian Institute of Technology Madras (IIT Madras), Chennai 600036, India
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Algorithms 2020, 13(1), 3; https://doi.org/10.3390/a13010003
Received: 11 November 2019 / Revised: 12 December 2019 / Accepted: 12 December 2019 / Published: 19 December 2019
(This article belongs to the Special Issue New Frontiers in Parameterized Complexity and Algorithms)
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. View Full-Text
Keywords: probabilistic graphs; uncertain graphs; influence maximization; cascade failure; linear reliable ordering; expected coverage; probabilistic core. probabilistic graphs; uncertain graphs; influence maximization; cascade failure; linear reliable ordering; expected coverage; probabilistic core.
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MDPI and ACS Style

Narayanaswamy, N.S.; Vijayaragunathan, R. Parameterized Optimization in Uncertain Graphs—A Survey and Some Results. Algorithms 2020, 13, 3. https://doi.org/10.3390/a13010003

AMA Style

Narayanaswamy NS, Vijayaragunathan R. Parameterized Optimization in Uncertain Graphs—A Survey and Some Results. Algorithms. 2020; 13(1):3. https://doi.org/10.3390/a13010003

Chicago/Turabian Style

Narayanaswamy, N. S.; Vijayaragunathan, R. 2020. "Parameterized Optimization in Uncertain Graphs—A Survey and Some Results" Algorithms 13, no. 1: 3. https://doi.org/10.3390/a13010003

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