Abstract Addressing a quest by Gupta et al. (in: Proceedings of the 41st international colloquium on automata, languages, and programming (ICALP 2014), vol 8572 of LNCS. Springer, pp 563–575, 2014), we provide a first, comprehensive study of finding a short s–t path in the multistage graph model, referred to as the Multistages–tPath problem. Herein, given a sequence of graphs over the same vertex set but changing edge sets, the task is to find short s–t paths in each graph (“snapshot”) such that in the found path sequence the consecutive s–t paths are “similar”. We measure similarity by the size of the symmetric difference of either the vertex set (vertex-similarity) or the edge set (edge-similarity) of any two consecutive paths. We prove that these two variants of Multistages–tPath are already $${\text {NP}}$$ NP -hard for an input sequence of only two snapshots and maximum vertex degree four. Motivated by this fact and natural applications of this scenario e.g. in traffic route planning, we perform a parameterized complexity analysis. Among other results, for both variants, vertex- and edge-similarity, we prove parameterized hardness ( $${\text {W[1]}}$$ W[1] -hardness) regarding the parameter path length (solution size). As a further conceptual investigation, we then modify the multistage model by asking for dissimilar consecutive paths. As one of the main technical results (employing so-called representative sets known from non-temporal settings), we prove that dissimilarity allows for fixed-parameter tractability for the parameter solution size, contrasting with our W[1]-hardness proof of the corresponding similarity case. We also provide partially positive results concerning efficient and effective data reduction (kernelization).

Following the increasing interest and adoption of FaaS systems, benchmarking frameworks for determining nonfunctional properties have also emerged. While existing (microbenchmark) frameworks only evaluate single aspects of FaaS platforms, a more holistic, application-driven approach is still missing. In this paper, we design and present BeFaaS, an extensible application-centric benchmarking framework for FaaS environments that focuses on the evaluation of FaaS platforms through realistic and typical examples of FaaS applications. BeFaaS includes a built-in e-commerce benchmark, is extensible for new workload profiles and new platforms, supports federated benchmark runs in which the benchmark application is distributed over multiple providers, and supports a fine-grained result analysis. Our evaluation compares three major FaaS providers in single cloud provider setups and shows that BeFaaS is capable of running each benchmark automatically with minimal configuration effort and providing detailed insights for each interaction.

Addressing a quest by Gupta et al. [ICALP'14], we provide a first, comprehensive study of finding a short s-t path in the multistage graph model, referred to as the Multistage s-t Path problem. Herein, given a sequence of graphs over the same vertex set but changing edge sets, the task is to find short s-t paths in each graph ("snapshot") such that in the found path sequence the consecutive s-t paths are "similar". We measure similarity by the size of the symmetric difference of either the vertex set (vertex-similarity) or the edge set (edge-similarity) of any two consecutive paths. We prove that these two variants of Multistage s-t Path are already NP-hard for an input sequence of only two graphs and maximum vertex degree four. Motivated by this fact and natural applications of this scenario e.g. in traffic route planning, we perform a parameterized complexity analysis. Among other results, for both variants, vertex- and edge-similarity, we prove parameterized hardness (W[1]-hardness) regarding the parameter path length (solution size) for both variants, vertex- and edge-similarity. As a further conceptual study, we then modify the multistage model by asking for dissimilar consecutive paths. One of our main technical results (employing so-called representative sets known from non-temporal settings) is that dissimilarity allows for fixed-parameter tractability for the parameter solution size, contrasting the W[1]-hardness of the corresponding similarity case. We also provide partially positive results concerning efficient and effective data reduction (kernelization).