Stability of Networks in Stretchable Graphs

Bilò, Davide; Gatto, Michael; Gualà, Luciano; Proietti, Guido; Widmayer, Peter

doi:10.1007/978-3-642-11476-2_9

Cited by 3 publications

References 7 publications

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“…This adaptation enables us to at least generate a feasible solution in all cases, while for robust optimization in general, feasibility cannot be guaranteed. Optimization for stable inputs attempts to understand when and how small changes in the input data affect the solution [8,9,10,11,12,13]. Regret minimization and online learning focuses on finding a good solution in an online setting, revealing one input after another, assuming an arbitrary adversary [14].…”

Section: Related Workmentioning

confidence: 99%

Robust optimization in the presence of uncertainty

Buhmann

Mihalák

Šrámek

et al. 2013

Proceedings of the 4th Conference on Innovations in Theoretical Computer Science

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We study optimization in the presence of uncertainty such as noise in measurements, and advocate a novel approach of tackling it. The main difference to any existing approach is that we do not assume any knowledge about the nature of the uncertainty (such as for instance a probability distribution). Instead, we are given several instances of the same optimization problem as input, and, assuming they are typical w.r.t. the uncertainty, we make use of it in order to compute a solution that is good for the sample instances as well as for future (unknown) typical instances.We demonstrate our approach for the case of two typical input instances. We first propose a measure of similarity of instances with respect to an objective. This concept allows us to assess whether instances are indeed typical. Based on this concept, we then choose a solution randomly among all solutions that are near-optimum for both instances. We show that the exact notion of near-optimum is intertwined with the proposed measure of similarity. Furthermore, we will show that our measure of similarity also allows us to derive formal statements about the expected quality of the computed solution: If the given instances are not similar, or are too noisy, our approach will detect this. We demonstrate for a few optimization problems and real world data that our approach works well not only in theory, but also in practice.

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Section: Related Workmentioning

confidence: 99%

Robust optimization in the presence of uncertainty

Buhmann

Mihalák

Šrámek

et al. 2013

Proceedings of the 4th Conference on Innovations in Theoretical Computer Science

Self Cite

View full text Add to dashboard Buy / Rent full text

show abstract

Section: G(v E W)mentioning

confidence: 99%

“…λ: An edge perturbation vector λ = λη m η=1 of λ-perturbation degree, i.e., λ ≤ λη ≤ 1, η = 1, • • • , m (Bilò et al, 2010). The definition is modified according to the strongest path problem of this work in contrast to the shortest path problem in (Bilò et al, 2010). The associated perturbed graph Gλ = G(V, E, wλ) is defined by multiplying the weights of the original G(V, E, w) by their associated perturbation value from λ.…”

Section: G(v E W)mentioning

confidence: 99%

“…Also, for the purpose of simplicity, the notation O is omitted from the δ (H) notation. The δ (H) is defined as the minimum value that for every edge perturbation λ of degree δ (H), H contains an optimal solution for the graph Gλ with respect to O (Bilò et al, 2010).…”

Section: G(v E W)mentioning

confidence: 99%

“…It is worth noting that the results of the MEIO models could suffer from uncertainty in the input data. In order to have a measure of the degree of variability and uncertainty of the results, we introduce a sensitivity analysis following that has been considered for the shortest path problem (Bilò et al, 2010;Buhmann et al, 2013;Srámek, 2013).…”

Section: Sensitivity Analysis Of the Strongest Pathmentioning

confidence: 99%

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A Multi-Entity Input Output (MEIO) Approach to Sustainability - Water-Energy-GHG (WEG) Footprint Statements in Use Cases from Auto and Telco Industries

Farrahi¹,

Farrahi²,

Mohamed³

2014

Preprint

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A new Input-Output model, called the Multi-Entity Input-Output (MEIO) model, is introduced to estimate the responsibility of entities and actors of an ecosystem on the footprint and actions of each other. It assumed that the ecosystem is comprised of end users, service providers, and utilities. The proposed MEIO modeling approach can be seen as a realization of the Everybody-in-the-Loop (EitL) framework, which promotes a sustainable future using behaviors and actions that are aware of their ubiquitous eco-socio-environment impacts. In this vision, the behavioral changes could be initiated by providing all actors with their footprint statement, which would be estimated using the MEIO models. First, a naive MEIO model is proposed in the form of a graph of actions and responsibility by considering interactions and goods transfers among the entities and actors along four channels. In this model, the unnormalized responsibility and also the final responsibility among the actors are introduced, and then are used to re-allocate immediate footprint of actors to those who are implicitly responsible. The footprint in the current model is limited to three major impacts: Water usage, Energy consumption, and GHG emissions. The naive model is then generalized to Provider-perspective (P-perspective) and End User-perspective (E-perspective) MEIO models in order to make it more suitable to cases where a large number of end users are served by a provider. The E-perspective modeling approach particularly allows estimating the footprint associated to a specific end user. In two use cases from the auto and Telco industries, it has been observed that the proposed MEIO models are practical and dependable in allocating footprint to the provider and also to the end user, while i) avoiding footprint leakage to the end users and ii) handling the large numbers end users. In addition, it will be shown that the MEIO models could implicitly provide some features of the Scope-3 and LCA approaches. This would make the MEIO models an interesting candidate for integrating and merging various concepts that are otherwise incompatible.

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Stability of Networks in Stretchable Graphs

Cited by 3 publications

References 7 publications

Robust optimization in the presence of uncertainty

Robust optimization in the presence of uncertainty

A Multi-Entity Input Output (MEIO) Approach to Sustainability - Water-Energy-GHG (WEG) Footprint Statements in Use Cases from Auto and Telco Industries

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