2026-07-22T20:50:17Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8333 2024-03-06T10:42:06Z ddc:004 open_access

Fine-grained I/O Complexity via Reductions: New Lower Bounds, Faster Algorithms, and a Time Hierarchy Demaine, Erik D. Lincoln, Andrea Liu, Quanquan C. Lynch, Jayson Vassilevska Williams, Virginia IO model Fine-grained Complexity Algorithms 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Erik D. Demaine and Andrea Lincoln and Quanquan C. Liu and Jayson Lynch and Virginia Vassilevska Williams 2018 Is Part Of LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2018.34 urn:nbn:de:0030-drops-83335 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.34 eng https://creativecommons.org/licenses/by/3.0/legalcode