License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ITCS.2018.34
URN: urn:nbn:de:0030-drops-83335
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Demaine, Erik D. ; Lincoln, Andrea ; Liu, Quanquan C. ; Lynch, Jayson ; Vassilevska Williams, Virginia

Fine-grained I/O Complexity via Reductions: New Lower Bounds, Faster Algorithms, and a Time Hierarchy

LIPIcs-ITCS-2018-34.pdf (0.6 MB)


This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity
(conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why the Longest Common Subsequence problem gets a savings of a factor of the size of cache times the length of a cache line, but no more. We take the reductions and techniques from complexity and fine-grained complexity and apply them to the I/O model to generate new (conditional) lower bounds as well as new faster algorithms. We also prove the existence of a time hierarchy for the I/O model, which motivates the fine-grained reductions.

- Using fine-grained reductions, we give an algorithm for distinguishing 2 vs. 3 diameter and radius that runs in O(|E|^2/(MB)) cache misses, which for sparse graphs improves over the previous O(|V|^2/B) running time.
- We give new reductions from radius and diameter to Wiener index and median. These reductions are new in both the RAM and I/O models.

- We show meaningful reductions between problems that have linear-time solutions in the RAM model. The reductions use low I/O complexity (typically O(n/B)), and thus help to finely capture between "I/O linear time" O(n/B) and RAM linear time O(n).

- We generate new I/O assumptions based on the difficulty of improving sparse graph problem running times in the I/O model. We create conjectures that the current best known algorithms for Single Source Shortest Paths (SSSP), diameter, and radius are optimal.

- From these I/O-model assumptions, we show that many of the known reductions in the word-RAM model can naturally extend to hold in the I/O model as well (e.g., a lower bound on the I/O complexity of Longest Common Subsequence that matches the best known running time).

- We prove an analog of the Time Hierarchy Theorem in the I/O model, further motivating the study of fine-grained algorithmic differences.

BibTeX - Entry

  author =	{Erik D. Demaine and Andrea Lincoln and Quanquan C. Liu and Jayson Lynch and Virginia Vassilevska Williams},
  title =	{{Fine-grained I/O Complexity via Reductions: New Lower Bounds, Faster Algorithms, and a Time Hierarchy}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{34:1--34:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Anna R. Karlin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-83335},
  doi =		{10.4230/LIPIcs.ITCS.2018.34},
  annote =	{Keywords: IO model, Fine-grained Complexity, Algorithms}

Keywords: IO model, Fine-grained Complexity, Algorithms
Collection: 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)
Issue Date: 2018
Date of publication: 12.01.2018

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