Parameterized Optimization in Uncertain Graphs—A Survey and Some Results
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 b...
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| Veröffentlicht in: | Algorithms 2020-01, Vol.13 (1), p.3 |
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| creator | Narayanaswamy, N. S. Vijayaragunathan, R. |
| description | 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. |
| doi_str_mv | 10.3390/a13010003 |
| format | Article |
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| issn | 1999-4893 1999-4893 |
| language | eng |
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| source | DOAJ Directory of Open Access Journals; MDPI - Multidisciplinary Digital Publishing Institute; EZB-FREE-00999 freely available EZB journals |
| subjects | Algorithms Graphs Mathematical models Optimization Parameterization Parameters Polynomials Probability distribution Proteins Random variables Semantics Social networks |
| title | Parameterized Optimization in Uncertain Graphs—A Survey and Some Results |
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