Improved sampling with applications to dynamic graph algorithms:
Abstract: "We state a new sampling lemma and use it to improve the running time of dynamic graph algorithms. For the dynamic connectivity problem the previously best randomized algorithm takes expected time O(log³ n) per update, amortized over [omega](m) updates. Using the new sampling lemma, w...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
København
1995
|
| Schriftenreihe: | Datalogisk Institut <København>: DIKU-Rapport
1995,26 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "We state a new sampling lemma and use it to improve the running time of dynamic graph algorithms. For the dynamic connectivity problem the previously best randomized algorithm takes expected time O(log³ n) per update, amortized over [omega](m) updates. Using the new sampling lemma, we improve its running time to O(log² n) on a RAM and O(log² n (1 + [epsilon][superscript log*n] / [epsilon]³ = O(log[superscript 2 + o(1)]n) on a pointer machine, where 0 <[epsilon] [<or =] 1. There exists a lower bound in the cell probe model for the time per operation of [omega](log n/ log log n) for this problem. Improved running times are achieved for the following dynamic problems: (1) O(log³ n) to maintain the bridges in a graph (the 2-edge connectivity problem); (2) O(k log² n) to maintain a minimum spanning tree in a graph with k different weights (the k-weight minimum spanning tree problem); (3) O(log² n log U/[epsilon]') to maintain a spanning tree whose weight is a (1 + [epsilon]')-approximation of the weight of the minimum spanning tree, where U is the maximum weight in the graph (the (1 + [epsilon]')-approximate minimum spanning tree problem); and (4) O(log² n) to test if the graph is bipartite (the bipartiteness-testing problem)." |
| Beschreibung: | 9 S. |
Internformat
MARC
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|---|---|---|---|
| 001 | BV011046431 | ||
| 003 | DE-604 | ||
| 005 | 19971219 | ||
| 007 | t | ||
| 008 | 961108s1995 |||| 00||| engod | ||
| 035 | |a (OCoLC)38435081 | ||
| 035 | |a (DE-599)BVBBV011046431 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G | ||
| 100 | 1 | |a Henzinger, Monika R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Improved sampling with applications to dynamic graph algorithms |c Monika R. Henzinger & Mikkel Thorup |
| 264 | 1 | |a København |c 1995 | |
| 300 | |a 9 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Datalogisk Institut <København>: DIKU-Rapport |v 1995,26 | |
| 520 | 3 | |a Abstract: "We state a new sampling lemma and use it to improve the running time of dynamic graph algorithms. For the dynamic connectivity problem the previously best randomized algorithm takes expected time O(log³ n) per update, amortized over [omega](m) updates. Using the new sampling lemma, we improve its running time to O(log² n) on a RAM and O(log² n (1 + [epsilon][superscript log*n] / [epsilon]³ = O(log[superscript 2 + o(1)]n) on a pointer machine, where 0 <[epsilon] [<or =] 1. There exists a lower bound in the cell probe model for the time per operation of [omega](log n/ log log n) for this problem. Improved running times are achieved for the following dynamic problems: (1) O(log³ n) to maintain the bridges in a graph (the 2-edge connectivity problem); (2) O(k log² n) to maintain a minimum spanning tree in a graph with k different weights (the k-weight minimum spanning tree problem); (3) O(log² n log U/[epsilon]') to maintain a spanning tree whose weight is a (1 + [epsilon]')-approximation of the weight of the minimum spanning tree, where U is the maximum weight in the graph (the (1 + [epsilon]')-approximate minimum spanning tree problem); and (4) O(log² n) to test if the graph is bipartite (the bipartiteness-testing problem)." | |
| 650 | 4 | |a Algorithms | |
| 650 | 4 | |a Machine theory | |
| 650 | 4 | |a Sampling (Statistics) | |
| 700 | 1 | |a Thorup, Mikkel |d 1973- |e Verfasser |0 (DE-588)1044557877 |4 aut | |
| 830 | 0 | |a Datalogisk Institut <København>: DIKU-Rapport |v 1995,26 |w (DE-604)BV010011493 |9 1995,26 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007397365 | ||
Datensatz im Suchindex
| _version_ | 1804125536195182592 |
|---|---|
| any_adam_object | |
| author | Henzinger, Monika R. Thorup, Mikkel 1973- |
| author_GND | (DE-588)1044557877 |
| author_facet | Henzinger, Monika R. Thorup, Mikkel 1973- |
| author_role | aut aut |
| author_sort | Henzinger, Monika R. |
| author_variant | m r h mr mrh m t mt |
| building | Verbundindex |
| bvnumber | BV011046431 |
| ctrlnum | (OCoLC)38435081 (DE-599)BVBBV011046431 |
| format | Book |
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| id | DE-604.BV011046431 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:03:07Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007397365 |
| oclc_num | 38435081 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 9 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| record_format | marc |
| series | Datalogisk Institut <København>: DIKU-Rapport |
| series2 | Datalogisk Institut <København>: DIKU-Rapport |
| spelling | Henzinger, Monika R. Verfasser aut Improved sampling with applications to dynamic graph algorithms Monika R. Henzinger & Mikkel Thorup København 1995 9 S. txt rdacontent n rdamedia nc rdacarrier Datalogisk Institut <København>: DIKU-Rapport 1995,26 Abstract: "We state a new sampling lemma and use it to improve the running time of dynamic graph algorithms. For the dynamic connectivity problem the previously best randomized algorithm takes expected time O(log³ n) per update, amortized over [omega](m) updates. Using the new sampling lemma, we improve its running time to O(log² n) on a RAM and O(log² n (1 + [epsilon][superscript log*n] / [epsilon]³ = O(log[superscript 2 + o(1)]n) on a pointer machine, where 0 <[epsilon] [<or =] 1. There exists a lower bound in the cell probe model for the time per operation of [omega](log n/ log log n) for this problem. Improved running times are achieved for the following dynamic problems: (1) O(log³ n) to maintain the bridges in a graph (the 2-edge connectivity problem); (2) O(k log² n) to maintain a minimum spanning tree in a graph with k different weights (the k-weight minimum spanning tree problem); (3) O(log² n log U/[epsilon]') to maintain a spanning tree whose weight is a (1 + [epsilon]')-approximation of the weight of the minimum spanning tree, where U is the maximum weight in the graph (the (1 + [epsilon]')-approximate minimum spanning tree problem); and (4) O(log² n) to test if the graph is bipartite (the bipartiteness-testing problem)." Algorithms Machine theory Sampling (Statistics) Thorup, Mikkel 1973- Verfasser (DE-588)1044557877 aut Datalogisk Institut <København>: DIKU-Rapport 1995,26 (DE-604)BV010011493 1995,26 |
| spellingShingle | Henzinger, Monika R. Thorup, Mikkel 1973- Improved sampling with applications to dynamic graph algorithms Datalogisk Institut <København>: DIKU-Rapport Algorithms Machine theory Sampling (Statistics) |
| title | Improved sampling with applications to dynamic graph algorithms |
| title_auth | Improved sampling with applications to dynamic graph algorithms |
| title_exact_search | Improved sampling with applications to dynamic graph algorithms |
| title_full | Improved sampling with applications to dynamic graph algorithms Monika R. Henzinger & Mikkel Thorup |
| title_fullStr | Improved sampling with applications to dynamic graph algorithms Monika R. Henzinger & Mikkel Thorup |
| title_full_unstemmed | Improved sampling with applications to dynamic graph algorithms Monika R. Henzinger & Mikkel Thorup |
| title_short | Improved sampling with applications to dynamic graph algorithms |
| title_sort | improved sampling with applications to dynamic graph algorithms |
| topic | Algorithms Machine theory Sampling (Statistics) |
| topic_facet | Algorithms Machine theory Sampling (Statistics) |
| volume_link | (DE-604)BV010011493 |
| work_keys_str_mv | AT henzingermonikar improvedsamplingwithapplicationstodynamicgraphalgorithms AT thorupmikkel improvedsamplingwithapplicationstodynamicgraphalgorithms |