kth.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Dynamic set cover: Improved amortized and worst-case update time
KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Theoretical Computer Science, TCS.ORCID iD: 0000-0003-4468-2675
2021 (English)In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery , 2021, p. 2537-2549Conference paper, Published paper (Refereed)
Abstract [en]

In the dynamic minimum set cover problem, a challenge is to minimize the update time while guaranteeing close to the optimal min(O(log n), f) approximation factor. (Throughout, m, n, f, and C are parameters denoting the maximum number of sets, number of elements, frequency, and the cost range.) In the high-frequency range, when f = Ω(log n), this was achieved by a deterministic O(log n)-approximation algorithm with O(f log n) amortized update time [Gupta et al. STOC'17]. In the low-frequency range, the line of work by Gupta et al. [STOC'17], Abboud et al. [STOC'19], and Bhattacharya et al. [ICALP'15, IPCO'17, FOCS'19] led to a deterministic (1 + ε)f-approximation algorithm with O(f log(Cn)/ε2) amortized update time. In this paper we improve the latter update time and provide the first bounds that subsume (and sometimes improve) the state-of-the-art dynamic vertex cover algorithms. We obtain: (1) (1 + ε)f-approximation ratio in O(f log2(Cn)/ε3) worst-case update time: No non-trivial worst-case update time was previously known for dynamic set cover. Our bound subsumes and improves by a logarithmic factor the O(log3 n/poly(ε)) worst-case update time for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1) by Bhattacharya et al. [SODA'17]. (2) (1 + ε)f-approximation ratio in O ((f2/ε3) + (f/ε2) log C) amortized update time: This result improves the previous O(f log(Cn)/ε2) update time bound for most values of f in the low-frequency range, i.e. whenever f = o(log n). It is the first that is independent of m and n. It subsumes the constant amortized update time of Bhattacharya and Kulkarni [SODA'19] for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1). These results are achieved by leveraging the approximate complementary slackness and background schedulers techniques. These techniques were used in the local update scheme for dynamic vertex cover. Our main technical contribution is to adapt these techniques within the global update scheme of Bhattacharya et al. [FOCS'19] for the dynamic set cover problem.

Place, publisher, year, edition, pages
Association for Computing Machinery , 2021. p. 2537-2549
Keywords [en]
Algorithms, Approximation factor, Approximation ratios, High frequency HF, Low frequency range, Minimum set cover problem, Set cover problem, State of the art, Technical contribution, Approximation algorithms
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:kth:diva-309244Scopus ID: 2-s2.0-85105346556OAI: oai:DiVA.org:kth-309244DiVA, id: diva2:1640692
Conference
32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, 10 January 2021 through 13 January 2021, Alexandria, Virtual
Note

QC 20220225

Part of proceedings ISBN: 9781611976465

Available from: 2022-02-25 Created: 2022-02-25 Last updated: 2022-06-25Bibliographically approved

Open Access in DiVA

No full text in DiVA

Scopus

Authority records

Na Nongkai, Danupon

Search in DiVA

By author/editor
Na Nongkai, Danupon
By organisation
Theoretical Computer Science, TCS
Computer Sciences

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 27 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf