Fragile Complexity of Comparison-Based Algorithms

Peyman Afshani, Rolf Fagerberg, David Mortan Grøne Hammer, Riko Jacob, Irina Kostitsyna, Ulrich Meyer, Manuel Penschuck, Nodari Sitchinava

Research output: Conference Article in Proceeding or Book/Report chapterArticle in proceedingsResearchpeer-review


We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes part in. We give a number of upper and lower bounds on the fragile complexity for fundamental problems, including Minimum, Selection, Sorting and Heap Construction. The results include both deterministic and randomized upper and lower bounds, and demonstrate a separation between the two settings for a number of problems. The depth of a comparator network is a straight-forward upper bound on the worst case fragile complexity of the corresponding fragile algorithm. We prove that fragile complexity is a different and strictly easier property than the depth of comparator networks, in the sense that for some problems a fragile complexity equal to the best network depth can be achieved with less total work and that with randomization, even a lower fragile complexity is possible.
Original languageEnglish
Title of host publication27th Annual European Symposium on Algorithms (ESA 2019)
PublisherSchloss Dagstuhl--Leibniz-Zentrum für Informatik
Publication date9 Sept 2019
Article number2
ISBN (Electronic)978-3-95977-124-5
Publication statusPublished - 9 Sept 2019
Event27th Annual European Symposium on Algorithms (ESA 2019) - Garching, Munich, Germany
Duration: 9 Sept 201911 Sept 2019
Conference number: 27


Conference27th Annual European Symposium on Algorithms (ESA 2019)
SeriesLeibniz International Proceedings in Informatics (LIPIcs)


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