License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2023.18
URN: urn:nbn:de:0030-drops-176703
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Capelli, Florent ; Strozecki, Yann

Geometric Amortization of Enumeration Algorithms

LIPIcs-STACS-2023-18.pdf (0.9 MB)


In this paper, we introduce a technique we call geometric amortization for enumeration algorithms, which can be used to make the delay of enumeration algorithms more regular with little overhead on the space it uses. More precisely, we consider enumeration algorithms having incremental linear delay, that is, algorithms enumerating, on input x, a set A(x) such that for every t ≤ ♯ A(x), it outputs at least t solutions in time O(t⋅p(|x|)), where p is a polynomial. We call p the incremental delay of the algorithm. While it is folklore that one can transform such an algorithm into an algorithm with maximal delay O(p(|x|)), the naive transformation may use exponential space. We show that, using geometric amortization, such an algorithm can be transformed into an algorithm with delay O(p(|x|)log(♯A(x))) and space O(s log(♯A(x))) where s is the space used by the original algorithm. In terms of complexity, we prove that classes DelayP and IncP₁ with polynomial space coincide.
We apply geometric amortization to show that one can trade the delay of flashlight search algorithms for their average delay up to a factor of O(log(♯A(x))). We illustrate how this tradeoff is advantageous for the enumeration of solutions of DNF formulas.

BibTeX - Entry

  author =	{Capelli, Florent and Strozecki, Yann},
  title =	{{Geometric Amortization of Enumeration Algorithms}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-176703},
  doi =		{10.4230/LIPIcs.STACS.2023.18},
  annote =	{Keywords: Enumeration, Polynomial Delay, Incremental Delay, Amortization}

Keywords: Enumeration, Polynomial Delay, Incremental Delay, Amortization
Collection: 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)
Issue Date: 2023
Date of publication: 03.03.2023
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