FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3133527322> ?p ?o ?g. }

• W3133527322 endingPage "2577" @default.
• W3133527322 startingPage "2552" @default.
• W3133527322 abstract "Abstract Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this area is deciding whether a given permutation of length n contains a given pattern of length k . In this work we give two new algorithms for this well-studied problem, one whose running time is $$n^{k/4 + o(k)}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msup><mml:mi>n</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>/</mml:mo><mml:mn>4</mml:mn><mml:mo>+</mml:mo><mml:mi>o</mml:mi><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:math> , and a polynomial-space algorithm whose running time is the better of $$O(1.6181^n)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>.</mml:mo><mml:msup><mml:mn>6181</mml:mn><mml:mi>n</mml:mi></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math> and $$O(n^{k/2 + 1})$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math> . These results improve the earlier best bounds of $$n^{0.47k + o(k)}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msup><mml:mi>n</mml:mi><mml:mrow><mml:mn>0.47</mml:mn><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mi>o</mml:mi><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:math> and $$O(1.79^n)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>.</mml:mo><mml:msup><mml:mn>79</mml:mn><mml:mi>n</mml:mi></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math> due to Ahal and Rabinovich (2000) resp. Bruner and Lackner (2012) and are the fastest algorithms for the problem when $$k in varOmega (log {n})$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>k</mml:mi><mml:mo>∈</mml:mo><mml:mi>Ω</mml:mi><mml:mo>(</mml:mo><mml:mo>log</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> . We show that both our new algorithms and the previous exponential-time algorithms in the literature can be viewed through the unifying lens of constraint-satisfaction . Our algorithms can also count , within the same running time, the number of occurrences of a pattern. We show that this result is close to optimal: solving the counting problem in time $$f(k) cdot n^{o(k/log {k})}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>·</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>/</mml:mo><mml:mo>log</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> would contradict the exponential-time hypothesis (ETH). For some special classes of patterns we obtain improved running times. We further prove that 3- increasing (4321-avoiding) and 3- decreasing (1234-avoiding) permutations can, in some sense, embed arbitrary permutations of almost linear length, which indicates that a sub-exponential running time is unlikely with the current techniques, even for patterns from these restricted classes." @default.
• W3133527322 created "2021-03-15" @default.
• W3133527322 creator A5012849997 @default.
• W3133527322 creator A5065214797 @default.
• W3133527322 creator A5065566770 @default.
• W3133527322 date "2021-03-01" @default.
• W3133527322 modified "2023-10-17" @default.
• W3133527322 title "Finding and Counting Permutations via CSPs" @default.
• W3133527322 cites W1803235859 @default.
• W3133527322 cites W1956214747 @default.
• W3133527322 cites W1995003166 @default.
• W3133527322 cites W1999038767 @default.
• W3133527322 cites W2005234139 @default.
• W3133527322 cites W2017788080 @default.
• W3133527322 cites W2038377288 @default.
• W3133527322 cites W2045499731 @default.
• W3133527322 cites W2052359455 @default.
• W3133527322 cites W2056944493 @default.
• W3133527322 cites W2058477139 @default.
• W3133527322 cites W2063191044 @default.
• W3133527322 cites W2066885472 @default.
• W3133527322 cites W2071490448 @default.
• W3133527322 cites W2077866342 @default.
• W3133527322 cites W2083275516 @default.
• W3133527322 cites W2083354900 @default.
• W3133527322 cites W2085041675 @default.
• W3133527322 cites W2087083200 @default.
• W3133527322 cites W2091015960 @default.
• W3133527322 cites W2102928439 @default.
• W3133527322 cites W2150004999 @default.
• W3133527322 cites W2154399201 @default.
• W3133527322 cites W2157509203 @default.
• W3133527322 cites W2157844376 @default.
• W3133527322 cites W2160859989 @default.
• W3133527322 cites W2170702810 @default.
• W3133527322 cites W2397978869 @default.
• W3133527322 cites W2485265215 @default.
• W3133527322 cites W2596359514 @default.
• W3133527322 cites W2810370675 @default.
• W3133527322 cites W2950143318 @default.
• W3133527322 cites W2963363569 @default.
• W3133527322 cites W2963368860 @default.
• W3133527322 cites W2963419264 @default.
• W3133527322 cites W2963533953 @default.
• W3133527322 cites W4212838771 @default.
• W3133527322 cites W4237930722 @default.
• W3133527322 cites W4247687185 @default.
• W3133527322 cites W4250463917 @default.
• W3133527322 doi "https://doi.org/10.1007/s00453-021-00812-z" @default.
• W3133527322 hasPublicationYear "2021" @default.
• W3133527322 type Work @default.
• W3133527322 sameAs 3133527322 @default.
• W3133527322 citedByCount "3" @default.
• W3133527322 countsByYear W31335273222021 @default.
• W3133527322 countsByYear W31335273222022 @default.
• W3133527322 countsByYear W31335273222023 @default.
• W3133527322 crossrefType "journal-article" @default.
• W3133527322 hasAuthorship W3133527322A5012849997 @default.
• W3133527322 hasAuthorship W3133527322A5065214797 @default.
• W3133527322 hasAuthorship W3133527322A5065566770 @default.
• W3133527322 hasBestOaLocation W31335273221 @default.
• W3133527322 hasConcept C11413529 @default.
• W3133527322 hasConcept C154945302 @default.
• W3133527322 hasConcept C41008148 @default.
• W3133527322 hasConceptScore W3133527322C11413529 @default.
• W3133527322 hasConceptScore W3133527322C154945302 @default.
• W3133527322 hasConceptScore W3133527322C41008148 @default.
• W3133527322 hasFunder F4320324521 @default.
• W3133527322 hasIssue "8" @default.
• W3133527322 hasLocation W31335273221 @default.
• W3133527322 hasLocation W31335273222 @default.
• W3133527322 hasLocation W31335273223 @default.
• W3133527322 hasLocation W31335273224 @default.
• W3133527322 hasLocation W31335273225 @default.
• W3133527322 hasOpenAccess W3133527322 @default.
• W3133527322 hasPrimaryLocation W31335273221 @default.
• W3133527322 hasRelatedWork W2003465964 @default.
• W3133527322 hasRelatedWork W2333698505 @default.
• W3133527322 hasRelatedWork W2351491280 @default.
• W3133527322 hasRelatedWork W2371447506 @default.
• W3133527322 hasRelatedWork W2386767533 @default.
• W3133527322 hasRelatedWork W2390279801 @default.
• W3133527322 hasRelatedWork W2748952813 @default.
• W3133527322 hasRelatedWork W2899084033 @default.
• W3133527322 hasRelatedWork W303980170 @default.
• W3133527322 hasRelatedWork W3107474891 @default.
• W3133527322 hasVolume "83" @default.
• W3133527322 isParatext "false" @default.
• W3133527322 isRetracted "false" @default.
• W3133527322 magId "3133527322" @default.
• W3133527322 workType "article" @default.