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Documents authored by Sitchinava, Nodari

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.5
The Impossibility of Simultaneous Time and I/O Optimality for the Planar Maxima and Convex Hull Problems

Authors: Peyman Afshani, Gerth Stølting Brodal, and Nodari Sitchinava

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
We prove that no deterministic output-sensitive algorithm for the planar convex hull and maxima problems can obtain both optimal time and I/O complexity, where the optimality is defined with respect to both the input and output sizes. This explains why the best previous algorithms achieved an optimal I/O bound at the cost of sub-optimal running time (Goodrich et al. [FOCS, 1993]). To the best of our knowledge, the impossibility of simultaneous optimality was only shown previously for the permutation problem by Brodal and Fagerberg [STOC, 2003]. Our results imply that no optimal deterministic output-sensitive cache-oblivious algorithm exists for either problem. In addition, we present simple deterministic algorithms that match our lower bounds and that provide a trade-off between time and I/Os. On the other hand, a simple modification of our deterministic algorithm results in a randomized algorithm that simultaneously achieves optimal (worst-case) time and optimal expected I/O bounds.
Cite as

Peyman Afshani, Gerth Stølting Brodal, and Nodari Sitchinava. The Impossibility of Simultaneous Time and I/O Optimality for the Planar Maxima and Convex Hull Problems. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{afshani_et_al:LIPIcs.ICALP.2026.5,
  author =	{Afshani, Peyman and Brodal, Gerth St{\o}lting and Sitchinava, Nodari},
  title =	{{The Impossibility of Simultaneous Time and I/O Optimality for the Planar Maxima and Convex Hull Problems}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.5},
  URN =		{urn:nbn:de:0030-drops-263943},
  doi =		{10.4230/LIPIcs.ICALP.2026.5},
  annote =	{Keywords: External Memory model, cache-oblivious algorithms, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.5
External-Memory Priority Queues with Optimal Insertions

Authors: Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We present an external-memory priority queue structure supporting Insert and DeleteMin with amortized 𝒪(1) and 𝒪(lg N) comparisons, respectively, and amortized 𝒪(1/B) and 𝒪(1/B log_{M/B} N/B) I/Os, respectively. Here, M is the size of the internal memory, B is the block size of I/Os between internal and external memory, and N is the number of elements in the priority queue just before an operation is performed. Previous external-memory priority queues required amortized 𝒪(lg N) comparisons and 𝒪(1/B log_{M/B} N/B) I/Os for both Insert and DeleteMin. The construction requires the minimal assumption M ≥ 2B.
Cite as

Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning. External-Memory Priority Queues with Optimal Insertions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brodal_et_al:LIPIcs.ESA.2025.5,
  author =	{Brodal, Gerth St{\o}lting and Goodrich, Michael T. and Iacono, John and Lo, Jared and Meyer, Ulrich and Pagan, Victor and Sitchinava, Nodari and Svenning, Rolf},
  title =	{{External-Memory Priority Queues with Optimal Insertions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.5},
  URN =		{urn:nbn:de:0030-drops-244734},
  doi =		{10.4230/LIPIcs.ESA.2025.5},
  annote =	{Keywords: priority queues, external memory, cache aware, amortized complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.2
Fragile Complexity of Comparison-Based Algorithms

Authors: Peyman Afshani, Rolf Fagerberg, David Hammer, Riko Jacob, Irina Kostitsyna, Ulrich Meyer, Manuel Penschuck, and Nodari Sitchinava

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
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.
Cite as

Peyman Afshani, Rolf Fagerberg, David Hammer, Riko Jacob, Irina Kostitsyna, Ulrich Meyer, Manuel Penschuck, and Nodari Sitchinava. Fragile Complexity of Comparison-Based Algorithms. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{afshani_et_al:LIPIcs.ESA.2019.2,
  author =	{Afshani, Peyman and Fagerberg, Rolf and Hammer, David and Jacob, Riko and Kostitsyna, Irina and Meyer, Ulrich and Penschuck, Manuel and Sitchinava, Nodari},
  title =	{{Fragile Complexity of Comparison-Based Algorithms}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{2:1--2:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.2},
  URN =		{urn:nbn:de:0030-drops-111235},
  doi =		{10.4230/LIPIcs.ESA.2019.2},
  annote =	{Keywords: Algorithms, comparison based algorithms, lower bounds}
}
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