Succinct and I/O Efficient Data Structures for Traversal in Trees

Abstract We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to...
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Autor*in:	Dillabaugh, Craig [verfasserIn] He, Meng [verfasserIn] Maheshwari, Anil [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2011

Schlagwörter:	Succinct data structures I/O efficient data structures Data structures Trees Path traversal

Übergeordnetes Werk:	Enthalten in: Algorithmica - New York, NY : Springer, 1986, 63(2011), 1-2 vom: 17. Mai, Seite 201-223
Übergeordnetes Werk:	volume:63 ; year:2011 ; number:1-2 ; day:17 ; month:05 ; pages:201-223

Links:	Volltext

DOI / URN:	10.1007/s00453-011-9528-z

Katalog-ID:	SPR00617261X

Internformat


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520			\|a Abstract We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. We show how a tree T on N nodes with q-bit keys, where q=O(lg N), can be blocked in a succinct fashion such that a bottom-up traversal requires O(K/B+1) I/Os using only $(2+q)N + q \cdot[ \frac{2 \tau N (q + 2 \lg B)}{w} + o(N)] + \frac{8\tau N \lg B}{w}$ bits to store T for any constant 0<τ<1, where K is the path length and w is the word size. This data structure is succinct because the above space cost is at most (2+q)N+q⋅(ηN+o(N)) bits for any arbitrarily selected constant, η, such that 0<η<1. When storing keys with tree nodes is not required, we can represent T in $2N + \frac{\epsilon N\lg B}{w} + o(N)$ bits, where ϵ is an arbitrarily selected constant such that 0<ϵ<1, while providing the same support for queries. Our second result is for top-down traversal in binary trees. We store the tree in (3+q)N+o(N) bits, while top-down traversal can still be performed in an asymptotically optimal number of I/Os.
650		4	\|a Succinct data structures \|7 (dpeaa)DE-He213
650		4	\|a I/O efficient data structures \|7 (dpeaa)DE-He213
650		4	\|a Data structures \|7 (dpeaa)DE-He213
650		4	\|a Trees \|7 (dpeaa)DE-He213
650		4	\|a Path traversal \|7 (dpeaa)DE-He213
700	1		\|a He, Meng \|e verfasserin \|4 aut
700	1		\|a Maheshwari, Anil \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Algorithmica \|d New York, NY : Springer, 1986 \|g 63(2011), 1-2 vom: 17. Mai, Seite 201-223 \|w (DE-627)253389704 \|w (DE-600)1458414-1 \|x 1432-0541 \|7 nnns
773	1	8	\|g volume:63 \|g year:2011 \|g number:1-2 \|g day:17 \|g month:05 \|g pages:201-223
856	4	0	\|u https://dx.doi.org/10.1007/s00453-011-9528-z \|z lizenzpflichtig \|3 Volltext
912			\|a GBV_USEFLAG_A
912			\|a SYSFLAG_A
912			\|a GBV_SPRINGER
912			\|a SSG-OPC-MAT
912			\|a SSG-OPC-ASE
912			\|a GBV_ILN_11
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_101
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_267
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 54.00 \|q ASE
951			\|a AR
952			\|d 63 \|j 2011 \|e 1-2 \|b 17 \|c 05 \|h 201-223

Indexfelder

author_variant	c d cd m h mh a m am
matchkey_str	article:14320541:2011----::ucntniefcetaatutrso
hierarchy_sort_str	2011
bklnumber	54.00
publishDate	2011
allfields	10.1007/s00453-011-9528-z doi (DE-627)SPR00617261X (SPR)s00453-011-9528-z-e DE-627 ger DE-627 rakwb eng 004 ASE 510 004 ASE 54.00 bkl Dillabaugh, Craig verfasserin aut Succinct and I/O Efficient Data Structures for Traversal in Trees 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. We show how a tree T on N nodes with q-bit keys, where q=O(lg N), can be blocked in a succinct fashion such that a bottom-up traversal requires O(K/B+1) I/Os using only $(2+q)N + q \cdot[ \frac{2 \tau N (q + 2 \lg B)}{w} + o(N)] + \frac{8\tau N \lg B}{w}$ bits to store T for any constant 0<τ<1, where K is the path length and w is the word size. This data structure is succinct because the above space cost is at most (2+q)N+q⋅(ηN+o(N)) bits for any arbitrarily selected constant, η, such that 0<η<1. When storing keys with tree nodes is not required, we can represent T in $2N + \frac{\epsilon N\lg B}{w} + o(N)$ bits, where ϵ is an arbitrarily selected constant such that 0<ϵ<1, while providing the same support for queries. Our second result is for top-down traversal in binary trees. We store the tree in (3+q)N+o(N) bits, while top-down traversal can still be performed in an asymptotically optimal number of I/Os. Succinct data structures (dpeaa)DE-He213 I/O efficient data structures (dpeaa)DE-He213 Data structures (dpeaa)DE-He213 Trees (dpeaa)DE-He213 Path traversal (dpeaa)DE-He213 He, Meng verfasserin aut Maheshwari, Anil verfasserin aut Enthalten in Algorithmica New York, NY : Springer, 1986 63(2011), 1-2 vom: 17. Mai, Seite 201-223 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:63 year:2011 number:1-2 day:17 month:05 pages:201-223 https://dx.doi.org/10.1007/s00453-011-9528-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.00 ASE AR 63 2011 1-2 17 05 201-223
spelling	10.1007/s00453-011-9528-z doi (DE-627)SPR00617261X (SPR)s00453-011-9528-z-e DE-627 ger DE-627 rakwb eng 004 ASE 510 004 ASE 54.00 bkl Dillabaugh, Craig verfasserin aut Succinct and I/O Efficient Data Structures for Traversal in Trees 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. We show how a tree T on N nodes with q-bit keys, where q=O(lg N), can be blocked in a succinct fashion such that a bottom-up traversal requires O(K/B+1) I/Os using only $(2+q)N + q \cdot[ \frac{2 \tau N (q + 2 \lg B)}{w} + o(N)] + \frac{8\tau N \lg B}{w}$ bits to store T for any constant 0<τ<1, where K is the path length and w is the word size. This data structure is succinct because the above space cost is at most (2+q)N+q⋅(ηN+o(N)) bits for any arbitrarily selected constant, η, such that 0<η<1. When storing keys with tree nodes is not required, we can represent T in $2N + \frac{\epsilon N\lg B}{w} + o(N)$ bits, where ϵ is an arbitrarily selected constant such that 0<ϵ<1, while providing the same support for queries. Our second result is for top-down traversal in binary trees. We store the tree in (3+q)N+o(N) bits, while top-down traversal can still be performed in an asymptotically optimal number of I/Os. Succinct data structures (dpeaa)DE-He213 I/O efficient data structures (dpeaa)DE-He213 Data structures (dpeaa)DE-He213 Trees (dpeaa)DE-He213 Path traversal (dpeaa)DE-He213 He, Meng verfasserin aut Maheshwari, Anil verfasserin aut Enthalten in Algorithmica New York, NY : Springer, 1986 63(2011), 1-2 vom: 17. Mai, Seite 201-223 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:63 year:2011 number:1-2 day:17 month:05 pages:201-223 https://dx.doi.org/10.1007/s00453-011-9528-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.00 ASE AR 63 2011 1-2 17 05 201-223
allfields_unstemmed	10.1007/s00453-011-9528-z doi (DE-627)SPR00617261X (SPR)s00453-011-9528-z-e DE-627 ger DE-627 rakwb eng 004 ASE 510 004 ASE 54.00 bkl Dillabaugh, Craig verfasserin aut Succinct and I/O Efficient Data Structures for Traversal in Trees 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. We show how a tree T on N nodes with q-bit keys, where q=O(lg N), can be blocked in a succinct fashion such that a bottom-up traversal requires O(K/B+1) I/Os using only $(2+q)N + q \cdot[ \frac{2 \tau N (q + 2 \lg B)}{w} + o(N)] + \frac{8\tau N \lg B}{w}$ bits to store T for any constant 0<τ<1, where K is the path length and w is the word size. This data structure is succinct because the above space cost is at most (2+q)N+q⋅(ηN+o(N)) bits for any arbitrarily selected constant, η, such that 0<η<1. When storing keys with tree nodes is not required, we can represent T in $2N + \frac{\epsilon N\lg B}{w} + o(N)$ bits, where ϵ is an arbitrarily selected constant such that 0<ϵ<1, while providing the same support for queries. Our second result is for top-down traversal in binary trees. We store the tree in (3+q)N+o(N) bits, while top-down traversal can still be performed in an asymptotically optimal number of I/Os. Succinct data structures (dpeaa)DE-He213 I/O efficient data structures (dpeaa)DE-He213 Data structures (dpeaa)DE-He213 Trees (dpeaa)DE-He213 Path traversal (dpeaa)DE-He213 He, Meng verfasserin aut Maheshwari, Anil verfasserin aut Enthalten in Algorithmica New York, NY : Springer, 1986 63(2011), 1-2 vom: 17. Mai, Seite 201-223 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:63 year:2011 number:1-2 day:17 month:05 pages:201-223 https://dx.doi.org/10.1007/s00453-011-9528-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.00 ASE AR 63 2011 1-2 17 05 201-223
allfieldsGer	10.1007/s00453-011-9528-z doi (DE-627)SPR00617261X (SPR)s00453-011-9528-z-e DE-627 ger DE-627 rakwb eng 004 ASE 510 004 ASE 54.00 bkl Dillabaugh, Craig verfasserin aut Succinct and I/O Efficient Data Structures for Traversal in Trees 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. We show how a tree T on N nodes with q-bit keys, where q=O(lg N), can be blocked in a succinct fashion such that a bottom-up traversal requires O(K/B+1) I/Os using only $(2+q)N + q \cdot[ \frac{2 \tau N (q + 2 \lg B)}{w} + o(N)] + \frac{8\tau N \lg B}{w}$ bits to store T for any constant 0<τ<1, where K is the path length and w is the word size. This data structure is succinct because the above space cost is at most (2+q)N+q⋅(ηN+o(N)) bits for any arbitrarily selected constant, η, such that 0<η<1. When storing keys with tree nodes is not required, we can represent T in $2N + \frac{\epsilon N\lg B}{w} + o(N)$ bits, where ϵ is an arbitrarily selected constant such that 0<ϵ<1, while providing the same support for queries. Our second result is for top-down traversal in binary trees. We store the tree in (3+q)N+o(N) bits, while top-down traversal can still be performed in an asymptotically optimal number of I/Os. Succinct data structures (dpeaa)DE-He213 I/O efficient data structures (dpeaa)DE-He213 Data structures (dpeaa)DE-He213 Trees (dpeaa)DE-He213 Path traversal (dpeaa)DE-He213 He, Meng verfasserin aut Maheshwari, Anil verfasserin aut Enthalten in Algorithmica New York, NY : Springer, 1986 63(2011), 1-2 vom: 17. Mai, Seite 201-223 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:63 year:2011 number:1-2 day:17 month:05 pages:201-223 https://dx.doi.org/10.1007/s00453-011-9528-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.00 ASE AR 63 2011 1-2 17 05 201-223
allfieldsSound	10.1007/s00453-011-9528-z doi (DE-627)SPR00617261X (SPR)s00453-011-9528-z-e DE-627 ger DE-627 rakwb eng 004 ASE 510 004 ASE 54.00 bkl Dillabaugh, Craig verfasserin aut Succinct and I/O Efficient Data Structures for Traversal in Trees 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. We show how a tree T on N nodes with q-bit keys, where q=O(lg N), can be blocked in a succinct fashion such that a bottom-up traversal requires O(K/B+1) I/Os using only $(2+q)N + q \cdot[ \frac{2 \tau N (q + 2 \lg B)}{w} + o(N)] + \frac{8\tau N \lg B}{w}$ bits to store T for any constant 0<τ<1, where K is the path length and w is the word size. This data structure is succinct because the above space cost is at most (2+q)N+q⋅(ηN+o(N)) bits for any arbitrarily selected constant, η, such that 0<η<1. When storing keys with tree nodes is not required, we can represent T in $2N + \frac{\epsilon N\lg B}{w} + o(N)$ bits, where ϵ is an arbitrarily selected constant such that 0<ϵ<1, while providing the same support for queries. Our second result is for top-down traversal in binary trees. We store the tree in (3+q)N+o(N) bits, while top-down traversal can still be performed in an asymptotically optimal number of I/Os. Succinct data structures (dpeaa)DE-He213 I/O efficient data structures (dpeaa)DE-He213 Data structures (dpeaa)DE-He213 Trees (dpeaa)DE-He213 Path traversal (dpeaa)DE-He213 He, Meng verfasserin aut Maheshwari, Anil verfasserin aut Enthalten in Algorithmica New York, NY : Springer, 1986 63(2011), 1-2 vom: 17. Mai, Seite 201-223 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:63 year:2011 number:1-2 day:17 month:05 pages:201-223 https://dx.doi.org/10.1007/s00453-011-9528-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.00 ASE AR 63 2011 1-2 17 05 201-223
language	English
source	Enthalten in Algorithmica 63(2011), 1-2 vom: 17. Mai, Seite 201-223 volume:63 year:2011 number:1-2 day:17 month:05 pages:201-223
sourceStr	Enthalten in Algorithmica 63(2011), 1-2 vom: 17. Mai, Seite 201-223 volume:63 year:2011 number:1-2 day:17 month:05 pages:201-223
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Succinct data structures I/O efficient data structures Data structures Trees Path traversal
dewey-raw	004
isfreeaccess_bool	false
container_title	Algorithmica
authorswithroles_txt_mv	Dillabaugh, Craig @@aut@@ He, Meng @@aut@@ Maheshwari, Anil @@aut@@
publishDateDaySort_date	2011-05-17T00:00:00Z
hierarchy_top_id	253389704
dewey-sort	14
id	SPR00617261X
language_de	englisch
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author	Dillabaugh, Craig
spellingShingle	Dillabaugh, Craig ddc 004 ddc 510 bkl 54.00 misc Succinct data structures misc I/O efficient data structures misc Data structures misc Trees misc Path traversal Succinct and I/O Efficient Data Structures for Traversal in Trees
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topic_title	004 ASE 510 004 ASE 54.00 bkl Succinct and I/O Efficient Data Structures for Traversal in Trees Succinct data structures (dpeaa)DE-He213 I/O efficient data structures (dpeaa)DE-He213 Data structures (dpeaa)DE-He213 Trees (dpeaa)DE-He213 Path traversal (dpeaa)DE-He213
topic	ddc 004 ddc 510 bkl 54.00 misc Succinct data structures misc I/O efficient data structures misc Data structures misc Trees misc Path traversal
topic_unstemmed	ddc 004 ddc 510 bkl 54.00 misc Succinct data structures misc I/O efficient data structures misc Data structures misc Trees misc Path traversal
topic_browse	ddc 004 ddc 510 bkl 54.00 misc Succinct data structures misc I/O efficient data structures misc Data structures misc Trees misc Path traversal
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title	Succinct and I/O Efficient Data Structures for Traversal in Trees
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title_full	Succinct and I/O Efficient Data Structures for Traversal in Trees
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title_sort	succinct and i/o efficient data structures for traversal in trees
title_auth	Succinct and I/O Efficient Data Structures for Traversal in Trees
abstract	Abstract We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. We show how a tree T on N nodes with q-bit keys, where q=O(lg N), can be blocked in a succinct fashion such that a bottom-up traversal requires O(K/B+1) I/Os using only $(2+q)N + q \cdot[ \frac{2 \tau N (q + 2 \lg B)}{w} + o(N)] + \frac{8\tau N \lg B}{w}$ bits to store T for any constant 0<τ<1, where K is the path length and w is the word size. This data structure is succinct because the above space cost is at most (2+q)N+q⋅(ηN+o(N)) bits for any arbitrarily selected constant, η, such that 0<η<1. When storing keys with tree nodes is not required, we can represent T in $2N + \frac{\epsilon N\lg B}{w} + o(N)$ bits, where ϵ is an arbitrarily selected constant such that 0<ϵ<1, while providing the same support for queries. Our second result is for top-down traversal in binary trees. We store the tree in (3+q)N+o(N) bits, while top-down traversal can still be performed in an asymptotically optimal number of I/Os.
abstractGer	Abstract We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. We show how a tree T on N nodes with q-bit keys, where q=O(lg N), can be blocked in a succinct fashion such that a bottom-up traversal requires O(K/B+1) I/Os using only $(2+q)N + q \cdot[ \frac{2 \tau N (q + 2 \lg B)}{w} + o(N)] + \frac{8\tau N \lg B}{w}$ bits to store T for any constant 0<τ<1, where K is the path length and w is the word size. This data structure is succinct because the above space cost is at most (2+q)N+q⋅(ηN+o(N)) bits for any arbitrarily selected constant, η, such that 0<η<1. When storing keys with tree nodes is not required, we can represent T in $2N + \frac{\epsilon N\lg B}{w} + o(N)$ bits, where ϵ is an arbitrarily selected constant such that 0<ϵ<1, while providing the same support for queries. Our second result is for top-down traversal in binary trees. We store the tree in (3+q)N+o(N) bits, while top-down traversal can still be performed in an asymptotically optimal number of I/Os.
abstract_unstemmed	Abstract We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in a tree on N nodes and traverses a path to the root. We show how a tree T on N nodes with q-bit keys, where q=O(lg N), can be blocked in a succinct fashion such that a bottom-up traversal requires O(K/B+1) I/Os using only $(2+q)N + q \cdot[ \frac{2 \tau N (q + 2 \lg B)}{w} + o(N)] + \frac{8\tau N \lg B}{w}$ bits to store T for any constant 0<τ<1, where K is the path length and w is the word size. This data structure is succinct because the above space cost is at most (2+q)N+q⋅(ηN+o(N)) bits for any arbitrarily selected constant, η, such that 0<η<1. When storing keys with tree nodes is not required, we can represent T in $2N + \frac{\epsilon N\lg B}{w} + o(N)$ bits, where ϵ is an arbitrarily selected constant such that 0<ϵ<1, while providing the same support for queries. Our second result is for top-down traversal in binary trees. We store the tree in (3+q)N+o(N) bits, while top-down traversal can still be performed in an asymptotically optimal number of I/Os.
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container_issue	1-2
title_short	Succinct and I/O Efficient Data Structures for Traversal in Trees
url	https://dx.doi.org/10.1007/s00453-011-9528-z
remote_bool	true
author2	He, Meng Maheshwari, Anil
author2Str	He, Meng Maheshwari, Anil
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doi_str	10.1007/s00453-011-9528-z
up_date	2024-07-03T21:19:49.086Z
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Succinct and I/O Efficient Data Structures for Traversal in Trees

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