Optimal per-edge processing times in the semi-streaming model
We present semi-streaming algorithms for basic graph problems that have optimal per-edge processing times and therefore surpass all previous semi-streaming algorithms for these tasks. The semi-streaming model, which is appropriate when dealing with massive graphs, forbids random access to the input...
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| Vydáno v: | Information processing letters Ročník 104; číslo 3; s. 106 - 112 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier B.V
31.10.2007
Elsevier Science Elsevier Sequoia S.A |
| Témata: | |
| ISSN: | 0020-0190, 1872-6119 |
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| Abstract | We present semi-streaming algorithms for basic graph problems that have optimal per-edge processing times and therefore surpass all previous semi-streaming algorithms for these tasks. The semi-streaming model, which is appropriate when dealing with massive graphs, forbids random access to the input and restricts the memory to
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bits.
Particularly, the formerly best per-edge processing times for finding the connected components and a bipartition are
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α
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, for determining
k-vertex and
k-edge connectivity
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and
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respectively for any constant
k and for computing a minimum spanning forest
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. All these time bounds we reduce to
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1
)
.
Every presented algorithm determines a solution asymptotically as fast as the best corresponding algorithm up to date in the classical RAM model, which therefore cannot convert the advantage of unlimited memory and random access into superior computing times for these problems. |
|---|---|
| AbstractList | We present semi-streaming algorithms for basic graph problems that have optimal per-edge processing times and therefore surpass all previous semi-streaming algorithms for these tasks. The semi-streaming model, which is appropriate when dealing with massive graphs, forbids random access to the input and restricts the memory to
O
(
n
⋅
polylog
n
)
bits.
Particularly, the formerly best per-edge processing times for finding the connected components and a bipartition are
O
(
α
(
n
)
)
, for determining
k-vertex and
k-edge connectivity
O
(
k
2
n
)
and
O
(
n
⋅
log
n
)
respectively for any constant
k and for computing a minimum spanning forest
O
(
log
n
)
. All these time bounds we reduce to
O
(
1
)
.
Every presented algorithm determines a solution asymptotically as fast as the best corresponding algorithm up to date in the classical RAM model, which therefore cannot convert the advantage of unlimited memory and random access into superior computing times for these problems. We present semi-streaming algorithms for basic graph problems that have optimal per-edge processing times and therefore surpass all previous semi-streaming algorithms for these tasks. The semi-streaming model, which is appropriate when dealing with massive graphs, forbids random access to the input and restricts the memory to ... bits. Particularly, the formerly best per-edge processing times for finding the connected components and a bipartition are ..., for determining k-vertex and k-edge connectivity ... and ... respectively for any constant k and for computing a minimum spanning forest ... All these time bounds we reduce ... Every presented algorithm determines a solution asymptotically as fast as the best corresponding algorithm up to date in the classical RAM model, which therefore cannot convert the advantage of unlimited memory and random access into superior computing times for these problems. (ProQuest: ... denotes formulae/symbols omitted.) |
| Author | Zelke, Mariano |
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| Cites_doi | 10.1145/265910.265914 10.1145/505241.505243 10.1145/355541.355562 10.1137/1.9781611970265 10.1007/BF01758778 10.1006/jcss.1995.1022 |
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| Keywords | Streaming algorithms Graph algorithms Per-edge processing time Access time Vertex Computer theory Random access memory Processing time Computing Random graph Input Graph connectivity Information processing Fast algorithm Algorithm analysis Graph algorithm |
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| References | Nagamochi, Ibaraki (bib009) 1992; 7 Eppstein, Galil, Italiano, Nissenzweig (bib003) 1997; 44 M. Zelke J. Feigenbaum, S. Kannan, A. McGregor, S. Suri, J. Zhang, Graph distances in the streaming model: The value of space, in: SODA 2005, pp. 745–754 time, Tech. Rep. TR99-23, Univ. of Texas at Austin, Austin, TX Feigenbaum, Kannan, McGregor, Suri, Zhang (bib004) 2004; vol. 3142 Chazelle (bib002) 2000; 47 Pettie, Ramachandran (bib011) 2002; 49 S. Pettie, Finding minimum spanning trees in Gabow (bib007) 2000 R.E. Tarjan, Data structures and network algorithms, CBMS-NSF Regional Conference Series in Applied Mathematics, 1983 Gabow (bib006) 1995; 50 Muthukrishnan (bib008) connectivity in the semi-streaming model, 2006. Available at Bollobás (bib001) 1979 Chazelle (10.1016/j.ipl.2007.06.004_bib002) 2000; 47 Bollobás (10.1016/j.ipl.2007.06.004_bib001) 1979 Gabow (10.1016/j.ipl.2007.06.004_bib007) 2000 10.1016/j.ipl.2007.06.004_bib005 10.1016/j.ipl.2007.06.004_bib013 Gabow (10.1016/j.ipl.2007.06.004_bib006) 1995; 50 10.1016/j.ipl.2007.06.004_bib012 10.1016/j.ipl.2007.06.004_bib010 Muthukrishnan (10.1016/j.ipl.2007.06.004_bib008) Eppstein (10.1016/j.ipl.2007.06.004_bib003) 1997; 44 Feigenbaum (10.1016/j.ipl.2007.06.004_bib004) 2004; vol. 3142 Nagamochi (10.1016/j.ipl.2007.06.004_bib009) 1992; 7 Pettie (10.1016/j.ipl.2007.06.004_bib011) 2002; 49 |
| References_xml | – reference: S. Pettie, Finding minimum spanning trees in – volume: 49 start-page: 16 year: 2002 end-page: 34 ident: bib011 article-title: An optimal minimum spanning tree algorithm publication-title: J. ACM – ident: bib008 article-title: Data streams: Algorithms and applications – volume: 50 start-page: 259 year: 1995 end-page: 273 ident: bib006 article-title: A matroid approach to finding edge connectivity and packing arborescences publication-title: J. Comput. System Sci. – reference: -connectivity in the semi-streaming model, 2006. Available at – volume: 7 start-page: 583 year: 1992 end-page: 596 ident: bib009 article-title: A linear time algorithm for finding a sparse publication-title: Algorithmica – reference: J. Feigenbaum, S. Kannan, A. McGregor, S. Suri, J. Zhang, Graph distances in the streaming model: The value of space, in: SODA 2005, pp. 745–754 – start-page: 410 year: 2000 end-page: 420 ident: bib007 article-title: Using expander graphs to find vertex connectivity publication-title: Proceedings of the 41st IEEE Symposium on Foundations of Computer Science – reference: R.E. Tarjan, Data structures and network algorithms, CBMS-NSF Regional Conference Series in Applied Mathematics, 1983 – volume: vol. 3142 start-page: 531 year: 2004 end-page: 543 ident: bib004 article-title: On graph problems in a semi-streaming model publication-title: ICALP 2004 – year: 1979 ident: bib001 article-title: Graph Theory, An Introductory Course – reference: M. Zelke, – volume: 47 start-page: 1028 year: 2000 end-page: 1047 ident: bib002 article-title: A minimum spanning tree algorithm with inverse-Ackermann type complexity publication-title: J. ACM – reference: time, Tech. Rep. TR99-23, Univ. of Texas at Austin, Austin, TX – volume: 44 start-page: 669 year: 1997 end-page: 696 ident: bib003 article-title: Sparsification—A technique for speeding up dynamic graph algorithms publication-title: J. ACM – ident: 10.1016/j.ipl.2007.06.004_bib005 – ident: 10.1016/j.ipl.2007.06.004_bib010 – volume: 44 start-page: 669 issue: 1 year: 1997 ident: 10.1016/j.ipl.2007.06.004_bib003 article-title: Sparsification—A technique for speeding up dynamic graph algorithms publication-title: J. ACM doi: 10.1145/265910.265914 – year: 1979 ident: 10.1016/j.ipl.2007.06.004_bib001 – volume: 49 start-page: 16 issue: 1 year: 2002 ident: 10.1016/j.ipl.2007.06.004_bib011 article-title: An optimal minimum spanning tree algorithm publication-title: J. ACM doi: 10.1145/505241.505243 – volume: 47 start-page: 1028 issue: 6 year: 2000 ident: 10.1016/j.ipl.2007.06.004_bib002 article-title: A minimum spanning tree algorithm with inverse-Ackermann type complexity publication-title: J. ACM doi: 10.1145/355541.355562 – ident: 10.1016/j.ipl.2007.06.004_bib012 doi: 10.1137/1.9781611970265 – ident: 10.1016/j.ipl.2007.06.004_bib013 – volume: 7 start-page: 583 year: 1992 ident: 10.1016/j.ipl.2007.06.004_bib009 article-title: A linear time algorithm for finding a sparse k-connected spanning subgraph of a k-connected graph publication-title: Algorithmica doi: 10.1007/BF01758778 – volume: vol. 3142 start-page: 531 year: 2004 ident: 10.1016/j.ipl.2007.06.004_bib004 article-title: On graph problems in a semi-streaming model – start-page: 410 year: 2000 ident: 10.1016/j.ipl.2007.06.004_bib007 article-title: Using expander graphs to find vertex connectivity – ident: 10.1016/j.ipl.2007.06.004_bib008 – volume: 50 start-page: 259 issue: 2 year: 1995 ident: 10.1016/j.ipl.2007.06.004_bib006 article-title: A matroid approach to finding edge connectivity and packing arborescences publication-title: J. Comput. System Sci. doi: 10.1006/jcss.1995.1022 |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Combinatorics Combinatorics. Ordered structures Computer science; control theory; systems Exact sciences and technology Graph algorithms Graph theory Graphs Information processing Information retrieval. Graph Mathematical models Mathematics Miscellaneous Per-edge processing time Random access memory Sciences and techniques of general use Streaming algorithms Studies Theoretical computing |
| Title | Optimal per-edge processing times in the semi-streaming model |
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