License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.67
URN: urn:nbn:de:0030-drops-124745
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12474/
Izumi, Taisuke ;
Otachi, Yota
Sublinear-Space Lexicographic Depth-First Search for Bounded Treewidth Graphs and Planar Graphs
Abstract
The lexicographic depth-first search (Lex-DFS) is one of the first basic graph problems studied in the context of space-efficient algorithms. It is shown independently by Asano et al. [ISAAC 2014] and Elmasry et al. [STACS 2015] that Lex-DFS admits polynomial-time algorithms that run with O(n)-bit working memory, where n is the number of vertices in the graph. Lex-DFS is known to be P-complete under logspace reduction, and giving or ruling out polynomial-time sublinear-space algorithms for Lex-DFS on general graphs is quite challenging. In this paper, we study Lex-DFS on graphs of bounded treewidth. We first show that given a tree decomposition of width O(n^(1-ε)) with ε > 0, Lex-DFS can be solved in sublinear space. We then complement this result by presenting a space-efficient algorithm that can compute, for w ≤ √n, a tree decomposition of width O(w √nlog n) or correctly decide that the graph has a treewidth more than w. This algorithm itself would be of independent interest as the first space-efficient algorithm for computing a tree decomposition of moderate (small but non-constant) width. By combining these results, we can show in particular that graphs of treewidth O(n^(1/2 - ε)) for some ε > 0 admits a polynomial-time sublinear-space algorithm for Lex-DFS. We can also show that planar graphs admit a polynomial-time algorithm with O(n^(1/2+ε))-bit working memory for Lex-DFS.
BibTeX - Entry
@InProceedings{izumi_et_al:LIPIcs:2020:12474,
author = {Taisuke Izumi and Yota Otachi},
title = {{Sublinear-Space Lexicographic Depth-First Search for Bounded Treewidth Graphs and Planar Graphs}},
booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
pages = {67:1--67:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-138-2},
ISSN = {1868-8969},
year = {2020},
volume = {168},
editor = {Artur Czumaj and Anuj Dawar and Emanuela Merelli},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12474},
URN = {urn:nbn:de:0030-drops-124745},
doi = {10.4230/LIPIcs.ICALP.2020.67},
annote = {Keywords: depth-first search, space complexity, treewidth}
}
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Keywords: |
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depth-first search, space complexity, treewidth |
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Collection: |
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47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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29.06.2020 |
