Space-Efficient Algorithms for Longest Increasing Subsequence
Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in O n log n time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For n ≤ s ≤ n , we present algor...
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| Published in: | Theory of computing systems Vol. 64; no. 3; pp. 522 - 541 |
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| Main Authors: | , , , , |
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| Language: | English |
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01.04.2020
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| Abstract | Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in
O
n
log
n
time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For
n
≤
s
≤
n
, we present algorithms that use
O
s
log
n
bits and
O
1
s
⋅
n
2
⋅
log
n
time for computing the length of a longest increasing subsequence, and
O
1
s
⋅
n
2
⋅
log
2
n
time for finding an actual subsequence. We also show that the time complexity of our algorithms is optimal up to polylogarithmic factors in the framework of sequential access algorithms with the prescribed amount of space. |
|---|---|
| AbstractList | Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in Onlogn time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For n≤s≤n, we present algorithms that use Oslogn bits and O1s⋅n2⋅logn time for computing the length of a longest increasing subsequence, and O1s⋅n2⋅log2n time for finding an actual subsequence. We also show that the time complexity of our algorithms is optimal up to polylogarithmic factors in the framework of sequential access algorithms with the prescribed amount of space. Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in O n log n time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For n ≤ s ≤ n , we present algorithms that use O s log n bits and O 1 s ⋅ n 2 ⋅ log n time for computing the length of a longest increasing subsequence, and O 1 s ⋅ n 2 ⋅ log 2 n time for finding an actual subsequence. We also show that the time complexity of our algorithms is optimal up to polylogarithmic factors in the framework of sequential access algorithms with the prescribed amount of space. |
| Author | Schweitzer, Pascal Tarui, Jun Kiyomi, Masashi Ono, Hirotaka Otachi, Yota |
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| Cites_doi | 10.1080/00207169708804607 10.1137/1.9781611973105.122 10.1007/978-3-642-38236-9_4 10.1137/130942152 10.1007/978-3-319-62389-4_1 10.1007/978-3-319-13075-0_44 10.1016/S0020-0190(00)00124-1 10.1145/359581.359603 10.1090/S0273-0979-99-00796-X 10.4230/LIPIcs.STACS.2015.288 10.1137/1004036 10.1016/0012-365X(75)90103-X 10.1017/CBO9781139872003 10.1007/978-3-662-44777-2_67 10.1016/j.ic.2010.04.003 10.1137/1005107 10.1137/1.9781611973730.83 10.1145/800135.804426 10.1007/s10878-006-7125-x 10.1016/0304-3975(80)90061-4 10.4153/CJM-1961-015-3 10.4230/LIPIcs.STACS.2016.57 10.1016/S0022-0000(70)80006-X 10.1137/0211022 10.4230/LIPIcs.ICALP.2016.58 10.1145/129712.129772 10.4230/LIPIcs.STACS.2017.9 10.1137/090770801 10.1016/0022-0000(87)90002-X 10.1007/978-3-662-44777-2_24 10.1007/s00454-006-1275-6 10.1109/SFCS.1998.743455 10.1007/s00493-014-3035-1 10.1007/978-3-319-62389-4_8 |
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| Keywords | Space-efficient algorithm Patience sorting Longest increasing subsequence |
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| References | Cook, S.A.: Deterministic CFL’s are accepted simultaneously in polynomial time and log squared space. In: STOC 1979, pp 338–345 (1979), https://doi.org/10.1145/800135.804426 ErgunFJowhariHOn the monotonicity of a data streamCombinatorica2015356641653343979010.1007/s00493-014-3035-11389.68037 Asano, T., Elmasry, A., Katajainen, J.: Priority queues and sorting for read-only data. In: TAMC 2013, pp 32–41 (2013). https://doi.org/10.1007/978-3-642-38236-9_4 MallowsCLProblem 62-2SIAM Rev.19635437537610.1137/1005107http://www.jstor.org/stable/2028347 KushilevitzENisanNCommunication complexity1997CambridgeCambridge University Press0869.68048 Gopalan, P., Jayram, T.S., Krauthgamer, R., Kumar, R.: Estimating the sortedness of a data stream. In: SODA 2007, pp 318–327 (2007). http://dl.acm.org/citation.cfm?id=1283417 Su, X., Woodruff, D.P.: The communication and streaming complexity of computing the longest common and increasing subsequences. In: SODA 2007, pp 336–345 (2007). http://dl.acm.org/citation.cfm?id=1283383.1283419 Pilipczuk, M., Wrochna, M.: On space efficiency of algorithms working on structural decompositions of graphs. In: STACS 2016, vol. 47, pp 57:1–57:15 (2016). https://doi.org/10.4230/LIPIcs.STACS.2016.57 Liben-NowellDVeeEAnZFinding longest increasing and common subsequences in streaming dataJ. Comb. Optim.2006112155175221291410.1007/s10878-006-7125-x1130.90040 RamananPTight $\Omega (n \lg n)$Ω(n lg n) lower bound for finding a longest increasing subsequenceInt. J. Comput. Math.1997653–4161164166951110.1080/002071697088046070890.68055 Asano, T., Izumi, T., Kiyomi, M., Konagaya, M., Ono, H., Otachi, Y., Schweitzer, P., Tarui, J., Uehara, R.: Depth-first search using O(n) bits. In: ISAAC 2014, pp 553–564 (2014). https://doi.org/10.1007/978-3-319-13075-0_44 BespamyatnikhSSegalMEnumerating longest increasing subsequences and patience sortingInf. Process. Lett.2000761–2711179755710.1016/S0020-0190(00)00124-11338.68205 MunroJIPatersonMSSelection and sorting with limited storageTheor. Comput. Sci.198012331532358931210.1016/0304-3975(80)90061-40441.68067 Naumovitz, T., Saks, M.: A polylogarithmic space deterministic streaming algorithm for approximating distance to monotonicity. In: SODA 2015, pp 1252–1262 (2015). https://doi.org/10.1137/1.9781611973730.83 Nisan, N.: RL ⊆\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\subseteq $\end{document} SC. In: STOC 1992, pp 619–623 (1992). https://doi.org/10.1145/129712.129772 Ahn, H.-K., Baraldo, N., Oh, E., Silvestri, F.: A time-space trade-off for triangulations of points in the plane. In: COCOON 2017, pp 3–12 (2017). https://doi.org/10.1007/978-3-319-62389-4_1 Saks, M., Seshadhri, C.: Space efficient streaming algorithms for the distance to monotonicity and asymmetric edit distance. In: SODA 2013, pp 1698–1709 (2013). https://doi.org/10.1137/1.9781611973105.122 Elmasry, A., Hagerup, T., Kammer, F.: Space-efficient basic graph algorithms. In: STACS 2015, vol. 30, pp 288–301 (2015). https://doi.org/10.4230/LIPIcs.STACS.2015.288 RomikDThe surprising mathematics of longest increasing subsequences2015CambridgeCambridge University Press1345.05003https://doi.org/10.1017/CBO9781139872003 Chakraborty, S., Satti, S.R.: Space-efficient algorithms for maximum cardinality search, stack BFS, queue BFS and applications. In: COCOON 2017, pp 87–98 (2017). https://doi.org/10.1007/978-3-319-62389-4_8 Lincoln, A., Williams, V.V., Wang, J.R., Ryan Williams, R.: Deterministic time-space trade-offs for k-SUM. In: ICALP 2016, pp 58:1–58:14 (2016), https://doi.org/10.4230/LIPIcs.ICALP.2016.58 MallowsCLPatience sortingBulletin of the Institute of Mathematics and its Applications19739216224 Pagter, J., Rauhe, T.: Optimal time-space trade-offs for sorting. In: FOCS 1998, pp 264–268 (1998). https://doi.org/10.1109/SFCS.1998.743455 SavitchWJRelationships between nondeterministic and deterministic tape complexitiesJ. Comput. Syst. Sci.19704217719226670210.1016/S0022-0000(70)80006-X0188.33502 BorodinACookSA time-space tradeoff for sorting on a general sequential model of computationSIAM J. Comput.198211228729765290310.1137/02110220478.68061 Darwish, O., Elmasry, A.: Optimal time-space tradeoff for the 2D convex-hull problem. In: ESA 2014, pp 284–295 (2014). https://doi.org/10.1007/978-3-662-44777-2_24 FredericksonGNUpper bounds for time-space trade-offs in sorting and selectionJ Comput Syst Sci1987341192688129210.1016/0022-0000(87)90002-X0642.68122 FredmanMLOn computing the length of longest increasing subsequencesDiscret. Math.1975111293535438610.1016/0012-365X(75)90103-X0312.68027 SchenstedCLongest increasing and decreasing subsequencesCan. J. Math.196113217919112130510.4153/CJM-1961-015-30097.25202 CrochemoreMPoratEFast computation of a longest increasing subsequence and applicationInf. Comput.2010208910541059268083610.1016/j.ic.2010.04.0031214.68479 Wang, J.R.: Space-efficient randomized algorithms for K-SUM. In: ESA 2014, pp 810–829 (2014). https://doi.org/10.1007/978-3-662-44777-2_67 AldousDDiaconisPLongest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theoremBull. Am. Math. Soc.1999364413432169420410.1090/S0273-0979-99-00796-Xhttps://doi.org/10.1090/S0273-0979-99-00796-X MallowsCLProblem 62-2, patience sortingSIAM Rev.19624214314910.1137/1004036http://www.jstor.org/stable/2028371 ChanTMChenEYMulti-pass geometric algorithmsDiscret. Comput. Geom.200737179102227986510.1007/s00454-006-1275-61106.68111 GálAGopalanPLower bounds on streaming algorithms for approximating the length of the longest increasing subsequenceSIAM J. Comput.201039834633479272161310.1137/090770801https://doi.org/10.1137/090770801 SaksMSeshadhriCEstimating the longest increasing sequence in polylogarithmic timeSIAM J. Comput.2017462774823363653710.1137/1309421521370.68342 Banyassady, B., Korman, M., Mulzer, W., Van Renssen, André, Roeloffzen, M., Seiferth, P., Stein, Y.: Improved time-space trade-offs for computing Voronoi diagrams. In: STACS 2017, vol. 66, pp 9:1–9:14 (2017). https://doi.org/10.4230/LIPIcs.STACS.2017.9 BursteinALankhamICombinatorics of patience sorting pilesSéminaire Lotharingien de Combinatoire200654AB54Ab22230261267.05005http://www.mat.univie.ac.at/∼slc/wpapers/s54Aburlank.html HuntJWSzymanskiTGA fast algorithm for computing longest common subsequencesCommun. ACM197720535035343665510.1145/359581.3596030354.68078 WJ Savitch (9908_CR36) 1970; 4 9908_CR9 JW Hunt (9908_CR20) 1977; 20 GN Frederickson (9908_CR16) 1987; 34 D Romik (9908_CR33) 2015 M Saks (9908_CR35) 2017; 46 F Ergun (9908_CR15) 2015; 35 9908_CR23 E Kushilevitz (9908_CR21) 1997 9908_CR28 9908_CR29 C Schensted (9908_CR37) 1961; 13 9908_CR1 ML Fredman (9908_CR17) 1975; 11 9908_CR3 9908_CR4 A Borodin (9908_CR7) 1982; 11 9908_CR5 A Burstein (9908_CR8) 2006; 54A P Ramanan (9908_CR32) 1997; 65 S Bespamyatnikh (9908_CR6) 2000; 76 JI Munro (9908_CR27) 1980; 12 D Liben-Nowell (9908_CR22) 2006; 11 D Aldous (9908_CR2) 1999; 36 CL Mallows (9908_CR26) 1973; 9 9908_CR31 9908_CR11 CL Mallows (9908_CR24) 1962; 4 9908_CR34 M Crochemore (9908_CR12) 2010; 208 9908_CR30 9908_CR39 9908_CR19 A Gál (9908_CR18) 2010; 39 9908_CR13 CL Mallows (9908_CR25) 1963; 5 TM Chan (9908_CR10) 2007; 37 9908_CR14 9908_CR38 |
| References_xml | – reference: SaksMSeshadhriCEstimating the longest increasing sequence in polylogarithmic timeSIAM J. Comput.2017462774823363653710.1137/1309421521370.68342 – reference: Wang, J.R.: Space-efficient randomized algorithms for K-SUM. In: ESA 2014, pp 810–829 (2014). https://doi.org/10.1007/978-3-662-44777-2_67 – reference: AldousDDiaconisPLongest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theoremBull. Am. Math. Soc.1999364413432169420410.1090/S0273-0979-99-00796-Xhttps://doi.org/10.1090/S0273-0979-99-00796-X – reference: Pilipczuk, M., Wrochna, M.: On space efficiency of algorithms working on structural decompositions of graphs. In: STACS 2016, vol. 47, pp 57:1–57:15 (2016). https://doi.org/10.4230/LIPIcs.STACS.2016.57 – reference: Elmasry, A., Hagerup, T., Kammer, F.: Space-efficient basic graph algorithms. In: STACS 2015, vol. 30, pp 288–301 (2015). https://doi.org/10.4230/LIPIcs.STACS.2015.288 – reference: Nisan, N.: RL ⊆\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\subseteq $\end{document} SC. In: STOC 1992, pp 619–623 (1992). https://doi.org/10.1145/129712.129772 – reference: HuntJWSzymanskiTGA fast algorithm for computing longest common subsequencesCommun. ACM197720535035343665510.1145/359581.3596030354.68078 – reference: Darwish, O., Elmasry, A.: Optimal time-space tradeoff for the 2D convex-hull problem. In: ESA 2014, pp 284–295 (2014). https://doi.org/10.1007/978-3-662-44777-2_24 – reference: GálAGopalanPLower bounds on streaming algorithms for approximating the length of the longest increasing subsequenceSIAM J. Comput.201039834633479272161310.1137/090770801https://doi.org/10.1137/090770801 – reference: Liben-NowellDVeeEAnZFinding longest increasing and common subsequences in streaming dataJ. Comb. Optim.2006112155175221291410.1007/s10878-006-7125-x1130.90040 – reference: Lincoln, A., Williams, V.V., Wang, J.R., Ryan Williams, R.: Deterministic time-space trade-offs for k-SUM. In: ICALP 2016, pp 58:1–58:14 (2016), https://doi.org/10.4230/LIPIcs.ICALP.2016.58 – reference: Pagter, J., Rauhe, T.: Optimal time-space trade-offs for sorting. In: FOCS 1998, pp 264–268 (1998). https://doi.org/10.1109/SFCS.1998.743455 – reference: Banyassady, B., Korman, M., Mulzer, W., Van Renssen, André, Roeloffzen, M., Seiferth, P., Stein, Y.: Improved time-space trade-offs for computing Voronoi diagrams. In: STACS 2017, vol. 66, pp 9:1–9:14 (2017). https://doi.org/10.4230/LIPIcs.STACS.2017.9 – reference: KushilevitzENisanNCommunication complexity1997CambridgeCambridge University Press0869.68048 – reference: SchenstedCLongest increasing and decreasing subsequencesCan. J. Math.196113217919112130510.4153/CJM-1961-015-30097.25202 – reference: Cook, S.A.: Deterministic CFL’s are accepted simultaneously in polynomial time and log squared space. In: STOC 1979, pp 338–345 (1979), https://doi.org/10.1145/800135.804426 – reference: ErgunFJowhariHOn the monotonicity of a data streamCombinatorica2015356641653343979010.1007/s00493-014-3035-11389.68037 – reference: FredericksonGNUpper bounds for time-space trade-offs in sorting and selectionJ Comput Syst Sci1987341192688129210.1016/0022-0000(87)90002-X0642.68122 – reference: Gopalan, P., Jayram, T.S., Krauthgamer, R., Kumar, R.: Estimating the sortedness of a data stream. In: SODA 2007, pp 318–327 (2007). http://dl.acm.org/citation.cfm?id=1283417 – reference: MallowsCLProblem 62-2, patience sortingSIAM Rev.19624214314910.1137/1004036http://www.jstor.org/stable/2028371 – reference: BursteinALankhamICombinatorics of patience sorting pilesSéminaire Lotharingien de Combinatoire200654AB54Ab22230261267.05005http://www.mat.univie.ac.at/∼slc/wpapers/s54Aburlank.html – reference: MallowsCLProblem 62-2SIAM Rev.19635437537610.1137/1005107http://www.jstor.org/stable/2028347 – reference: RamananPTight $\Omega (n \lg n)$Ω(n lg n) lower bound for finding a longest increasing subsequenceInt. J. Comput. Math.1997653–4161164166951110.1080/002071697088046070890.68055 – reference: Naumovitz, T., Saks, M.: A polylogarithmic space deterministic streaming algorithm for approximating distance to monotonicity. In: SODA 2015, pp 1252–1262 (2015). https://doi.org/10.1137/1.9781611973730.83 – reference: Asano, T., Elmasry, A., Katajainen, J.: Priority queues and sorting for read-only data. In: TAMC 2013, pp 32–41 (2013). https://doi.org/10.1007/978-3-642-38236-9_4 – reference: MunroJIPatersonMSSelection and sorting with limited storageTheor. Comput. Sci.198012331532358931210.1016/0304-3975(80)90061-40441.68067 – reference: RomikDThe surprising mathematics of longest increasing subsequences2015CambridgeCambridge University Press1345.05003https://doi.org/10.1017/CBO9781139872003 – reference: Su, X., Woodruff, D.P.: The communication and streaming complexity of computing the longest common and increasing subsequences. In: SODA 2007, pp 336–345 (2007). http://dl.acm.org/citation.cfm?id=1283383.1283419 – reference: Ahn, H.-K., Baraldo, N., Oh, E., Silvestri, F.: A time-space trade-off for triangulations of points in the plane. In: COCOON 2017, pp 3–12 (2017). https://doi.org/10.1007/978-3-319-62389-4_1 – reference: MallowsCLPatience sortingBulletin of the Institute of Mathematics and its Applications19739216224 – reference: SavitchWJRelationships between nondeterministic and deterministic tape complexitiesJ. Comput. Syst. Sci.19704217719226670210.1016/S0022-0000(70)80006-X0188.33502 – reference: Asano, T., Izumi, T., Kiyomi, M., Konagaya, M., Ono, H., Otachi, Y., Schweitzer, P., Tarui, J., Uehara, R.: Depth-first search using O(n) bits. In: ISAAC 2014, pp 553–564 (2014). https://doi.org/10.1007/978-3-319-13075-0_44 – reference: Chakraborty, S., Satti, S.R.: Space-efficient algorithms for maximum cardinality search, stack BFS, queue BFS and applications. In: COCOON 2017, pp 87–98 (2017). https://doi.org/10.1007/978-3-319-62389-4_8 – reference: CrochemoreMPoratEFast computation of a longest increasing subsequence and applicationInf. Comput.2010208910541059268083610.1016/j.ic.2010.04.0031214.68479 – reference: Saks, M., Seshadhri, C.: Space efficient streaming algorithms for the distance to monotonicity and asymmetric edit distance. In: SODA 2013, pp 1698–1709 (2013). https://doi.org/10.1137/1.9781611973105.122 – reference: BespamyatnikhSSegalMEnumerating longest increasing subsequences and patience sortingInf. Process. Lett.2000761–2711179755710.1016/S0020-0190(00)00124-11338.68205 – reference: FredmanMLOn computing the length of longest increasing subsequencesDiscret. Math.1975111293535438610.1016/0012-365X(75)90103-X0312.68027 – reference: ChanTMChenEYMulti-pass geometric algorithmsDiscret. Comput. Geom.200737179102227986510.1007/s00454-006-1275-61106.68111 – reference: BorodinACookSA time-space tradeoff for sorting on a general sequential model of computationSIAM J. Comput.198211228729765290310.1137/02110220478.68061 – volume: 65 start-page: 161 issue: 3–4 year: 1997 ident: 9908_CR32 publication-title: Int. J. Comput. Math. doi: 10.1080/00207169708804607 – ident: 9908_CR34 doi: 10.1137/1.9781611973105.122 – volume: 9 start-page: 216 year: 1973 ident: 9908_CR26 publication-title: Bulletin of the Institute of Mathematics and its Applications – ident: 9908_CR3 doi: 10.1007/978-3-642-38236-9_4 – volume: 46 start-page: 774 issue: 2 year: 2017 ident: 9908_CR35 publication-title: SIAM J. Comput. doi: 10.1137/130942152 – ident: 9908_CR1 doi: 10.1007/978-3-319-62389-4_1 – ident: 9908_CR4 doi: 10.1007/978-3-319-13075-0_44 – volume: 76 start-page: 7 issue: 1–2 year: 2000 ident: 9908_CR6 publication-title: Inf. Process. Lett. doi: 10.1016/S0020-0190(00)00124-1 – volume: 20 start-page: 350 issue: 5 year: 1977 ident: 9908_CR20 publication-title: Commun. ACM doi: 10.1145/359581.359603 – volume: 36 start-page: 413 issue: 4 year: 1999 ident: 9908_CR2 publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0273-0979-99-00796-X – volume: 54A start-page: B54Ab year: 2006 ident: 9908_CR8 publication-title: Séminaire Lotharingien de Combinatoire – ident: 9908_CR14 doi: 10.4230/LIPIcs.STACS.2015.288 – volume: 4 start-page: 143 issue: 2 year: 1962 ident: 9908_CR24 publication-title: SIAM Rev. doi: 10.1137/1004036 – volume: 11 start-page: 29 issue: 1 year: 1975 ident: 9908_CR17 publication-title: Discret. Math. doi: 10.1016/0012-365X(75)90103-X – volume-title: The surprising mathematics of longest increasing subsequences year: 2015 ident: 9908_CR33 doi: 10.1017/CBO9781139872003 – ident: 9908_CR39 doi: 10.1007/978-3-662-44777-2_67 – volume: 208 start-page: 1054 issue: 9 year: 2010 ident: 9908_CR12 publication-title: Inf. Comput. doi: 10.1016/j.ic.2010.04.003 – volume: 5 start-page: 375 issue: 4 year: 1963 ident: 9908_CR25 publication-title: SIAM Rev. doi: 10.1137/1005107 – ident: 9908_CR28 doi: 10.1137/1.9781611973730.83 – ident: 9908_CR11 doi: 10.1145/800135.804426 – ident: 9908_CR19 – volume: 11 start-page: 155 issue: 2 year: 2006 ident: 9908_CR22 publication-title: J. Comb. Optim. doi: 10.1007/s10878-006-7125-x – volume: 12 start-page: 315 issue: 3 year: 1980 ident: 9908_CR27 publication-title: Theor. Comput. Sci. doi: 10.1016/0304-3975(80)90061-4 – volume: 13 start-page: 179 issue: 2 year: 1961 ident: 9908_CR37 publication-title: Can. J. Math. doi: 10.4153/CJM-1961-015-3 – ident: 9908_CR31 doi: 10.4230/LIPIcs.STACS.2016.57 – volume: 4 start-page: 177 issue: 2 year: 1970 ident: 9908_CR36 publication-title: J. Comput. Syst. Sci. doi: 10.1016/S0022-0000(70)80006-X – volume: 11 start-page: 287 issue: 2 year: 1982 ident: 9908_CR7 publication-title: SIAM J. Comput. doi: 10.1137/0211022 – ident: 9908_CR38 – ident: 9908_CR23 doi: 10.4230/LIPIcs.ICALP.2016.58 – ident: 9908_CR29 doi: 10.1145/129712.129772 – volume-title: Communication complexity year: 1997 ident: 9908_CR21 – ident: 9908_CR5 doi: 10.4230/LIPIcs.STACS.2017.9 – volume: 39 start-page: 3463 issue: 8 year: 2010 ident: 9908_CR18 publication-title: SIAM J. Comput. doi: 10.1137/090770801 – volume: 34 start-page: 19 issue: 1 year: 1987 ident: 9908_CR16 publication-title: J Comput Syst Sci doi: 10.1016/0022-0000(87)90002-X – ident: 9908_CR13 doi: 10.1007/978-3-662-44777-2_24 – volume: 37 start-page: 79 issue: 1 year: 2007 ident: 9908_CR10 publication-title: Discret. Comput. Geom. doi: 10.1007/s00454-006-1275-6 – ident: 9908_CR30 doi: 10.1109/SFCS.1998.743455 – volume: 35 start-page: 641 issue: 6 year: 2015 ident: 9908_CR15 publication-title: Combinatorica doi: 10.1007/s00493-014-3035-1 – ident: 9908_CR9 doi: 10.1007/978-3-319-62389-4_8 |
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time... Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in Onlogn time and... |
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