Sensitivity analysis for shortest path problems and maximum capacity path problems in undirected graphs

Ramaswamy, Ramkumar; Orlin, James B.; Chakravarti, Nilopal

doi:10.1007/s10107-004-0517-8

Cited by 33 publications

(6 citation statements)

References 20 publications

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“…Algorithms for upper and lower tolerances for shortest paths and for maximum capacity paths were given in [41] by reducing these problems to the same problem, called Minimum Cost Interval problem. In [27], an algorithm was given that computes how much the length of the shortest path changes when an arbitrary link disappears.…”

Section: Traffic Redirection Attacksmentioning

confidence: 99%

Path Problems in Networks

Baras

Theodorakopoulos

2010

Synthesis Lectures on Communication Networks

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Synthesis Lectures on Communication Networks is an ongoing series of 50-to 100-page publications on topics on the design, implementation, and management of communication networks. Each lecture is a self-contained presentation of one topic by a leading expert. The topics range from algorithms to hardware implementations and cover a broad spectrum of issues from security to multiple-access protocols. The series addresses technologies from sensor networks to reconfigurable optical networks. The series is designed to: • Provide the best available presentations of important aspects of communication networks. • Help engineers and advanced students keep up with recent developments in a rapidly evolving technology. • Facilitate the development of courses in this field.

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Section: Traffic Redirection Attacksmentioning

confidence: 99%

Path Problems in Networks

Baras

Theodorakopoulos

2010

Synthesis Lectures on Communication Networks

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“…Without a priori knowledge of the uncertainty, Lin and Wen (2003) and Volgenant (2006) present the sensitivity of the linear assignment to perturbations in a single weight, based on the dual variables arising from a primal-dual optimisation. Ramaswamy et al (2005) provide similar results in the shortest path and maximum cut network problems, which can be shown to be equivalent formulations to the linear assignment problem. However, they do not consider simultaneous weight perturbations in multiple edges.…”

Section: Literature Reviewmentioning

confidence: 66%

Sensitivity Analysis for Bottleneck Assignment Problems

Elad¹,

Wood²,

Manzie³

et al. 2021

Preprint

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In assignment problems, decision makers are often interested in not only the optimal assignment, but also the sensitivity of the optimal assignment to perturbations in the assignment weights. Typically, only perturbations to individual assignment weights are considered. We present a novel extension of the traditional sensitivity analysis by allowing for simultaneous variations in all assignment weights. Focusing on the bottleneck assignment problem, we provide two different methods of quantifying the sensitivity of the optimal assignment, and present algorithms for each. Numerical examples as well as a discussion of the complexity for all algorithms are provided.

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“…In our approach, we obtain the inequalities in Eqn 2 by using the following observation: if the cost of an edge e * ∈ P * crosses the upper threshold β * e or an edge e ∈ P * falls below the lower threshold α e , all the other edge cost being fixed P * is no longer the shortest path from s to t. Therefore the condition for P * being the shortest path is Upper and lower shortest path tolerances are presented in [25] as:…”

Section: Deriving Systems Of Inequalitiesmentioning

confidence: 99%

Interactive Storytelling over Document Collections

Maiti¹,

Islam²,

Leman³

et al. 2016

Preprint

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Storytelling algorithms aim to 'connect the dots' between disparate documents by linking starting and ending documents through a series of intermediate documents. Existing storytelling algorithms are based on notions of coherence and connectivity, and thus the primary way by which users can steer the story construction is via design of suitable similarity functions. We present an alternative approach to storytelling wherein the user can interactively and iteratively provide 'must use' constraints to preferentially support the construction of some stories over others. The three innovations in our approach are distance measures based on (inferred) topic distributions, the use of constraints to define sets of linear inequalities over paths, and the introduction of slack and surplus variables to condition the topic distribution to preferentially emphasize desired terms over others. We describe experimental results to illustrate the effectiveness of our interactive storytelling approach over multiple text datasets.

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Sensitivity analysis for shortest path problems and maximum capacity path problems in undirected graphs

Cited by 33 publications

References 20 publications

Path Problems in Networks

Path Problems in Networks

Sensitivity Analysis for Bottleneck Assignment Problems

Interactive Storytelling over Document Collections

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