Sachit Malhotra

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Network Security has gained an ever increasing importance today because of the increased dependence on the networks. One way to assess the threats to the networks is through the use of the attack graphs. However, because of their sheer enormity and complexity the analysis becomes difficult. Given an attack graph the identification of a probable attack path(More)
Alternating Direction Implicit (ADI) methods are very good smoothers for multigrid. Like multigrid itself, ADI propagates information very quickly across a grid. On parallel processors, ADI is very ine cient due to the tridiagonal solves in each of the spatial directions. In one direction, the data typically resides in one processor. In the other(More)
In todaypsilas large complex organizational network, security administration is a challenging task. The typical means by which an attacker breaks into a network is through a series of exploits, where each exploit in the series satisfies the pre-condition for subsequent exploits and makes a causal relationship among them. Such a series of exploit is called(More)
Alternating direction iterative (ADI) methods do not usually work well on parallel computers due to having to do parallel rather than serial tridiagonal solves in all but one dimension. An ADI-like iteration is developed and analyzed which does not require parallel tridiagonal solves in any direction, has at least as good of a convergence rate as ADI, and(More)
Many problems based on unstructured grids provide a natural multigrid framework due to using an adaptive gridding procedure. When the grids are saved, even starting from just a ne grid problem poses no serious theoretical di culties in applying multigrid. A more di cult case occurs when a highly unstructured grid problem is to be solved with no hints how(More)
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