Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
A decomposition algorithm for network reliability evaluation
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Reliability of partialk-tree networks
Reliability of partialk-tree networks
An approximate algorithm for three-criteria replica allocation problem in WAN
PDCN '08 Proceedings of the IASTED International Conference on Parallel and Distributed Computing and Networks
Tree decompositions of graphs: Saving memory in dynamic programming
Discrete Optimization
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In this paper, we consider problems related to the network reliability problem, restricted to graphs of bounded treewidth. We look at undirected simple graphs with each vertex and edge a number in [0, 1] associated. These graphs model networks in which sites and links can fail, with a given probability, independently of whether other sites or links fail or not. The number in [0, 1] associated to each element is the probability that this element does not fail. In addition, there are distinguished sets of vertices: a set S of servers, and a set L of clients.This paper presents a dynamic programming framework for graphs of bounded treewidth for computing for a large number of different properties Y whether Y holds for the graph formed by the nodes and edges that did not fail. For instance, it is shown that one can compute in linear time the probability that all clients are connected to at least one server, assuming the treewidth of the input graph is bounded. The classical S- terminal reliability problem can be solved in linear time as well using this framework. The method is applicable to a large number of related questions. Depending on the particular problem, the algorithm obtained by the method uses linear, polynomial, or exponential time.