Finding cores of limited length:
Abstract: "In this paper we consider the problem of finding a core of limited length in a tree. A core is a path, which minimizes the sum of the distances to all nodes in the tree. This problem has been examined under different constraints on the tree and on the set of paths, from which the cor...
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
København
1997
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| Series: | Datalogisk Institut <København>: DIKU-Rapport
1997,3 |
| Subjects: | |
| Summary: | Abstract: "In this paper we consider the problem of finding a core of limited length in a tree. A core is a path, which minimizes the sum of the distances to all nodes in the tree. This problem has been examined under different constraints on the tree and on the set of paths, from which the core can be chosen. For all cases, we present linear or almost linear time algorithms, which improves the previous results. As Minieka and Patel observes [sic] (J. Algorithms, Vol. 4, 1983), the problem of finding a core of limited length would be simplified, if the core always contained the median, m. They conclude their paper by writing 'we do not know if a core of length l will contain m. Unfortunately, this situation remains unexplored and as this question remains open, the development of an efficient algorithm for locating a core of a specified length remains a difficult problem.' We show that the median is not necessarily included in the core and give an O(n min [log n[alpha](n, n), l]) algorithm for the problem, which improves the former best result O(n min [n², l log n])(Lo and Peng, J. Algorithms Vol. 20, 1996 and Minieka, Networks Vol, 15, 1985)." |
| Physical Description: | 10 S. |
Staff View
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| 520 | 3 | |a Abstract: "In this paper we consider the problem of finding a core of limited length in a tree. A core is a path, which minimizes the sum of the distances to all nodes in the tree. This problem has been examined under different constraints on the tree and on the set of paths, from which the core can be chosen. For all cases, we present linear or almost linear time algorithms, which improves the previous results. As Minieka and Patel observes [sic] (J. Algorithms, Vol. 4, 1983), the problem of finding a core of limited length would be simplified, if the core always contained the median, m. They conclude their paper by writing 'we do not know if a core of length l will contain m. Unfortunately, this situation remains unexplored and as this question remains open, the development of an efficient algorithm for locating a core of a specified length remains a difficult problem.' We show that the median is not necessarily included in the core and give an O(n min [log n[alpha](n, n), l]) algorithm for the problem, which improves the former best result O(n min [n², l log n])(Lo and Peng, J. Algorithms Vol. 20, 1996 and Minieka, Networks Vol, 15, 1985)." | |
| 650 | 4 | |a Combinatorial optimization | |
| 650 | 4 | |a Paths and cycles (Graph theory) | |
| 650 | 4 | |a Trees (Graph theory) | |
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| 830 | 0 | |a Datalogisk Institut <København>: DIKU-Rapport |v 1997,3 |w (DE-604)BV010011493 |9 1997,3 | |
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| id | DE-604.BV012174736 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:23:02Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008249036 |
| oclc_num | 38584661 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | 10 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
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| series | Datalogisk Institut <København>: DIKU-Rapport |
| series2 | Datalogisk Institut <København>: DIKU-Rapport |
| spelling | Finding cores of limited length Stephen Alstrup ... København 1997 10 S. txt rdacontent n rdamedia nc rdacarrier Datalogisk Institut <København>: DIKU-Rapport 1997,3 Abstract: "In this paper we consider the problem of finding a core of limited length in a tree. A core is a path, which minimizes the sum of the distances to all nodes in the tree. This problem has been examined under different constraints on the tree and on the set of paths, from which the core can be chosen. For all cases, we present linear or almost linear time algorithms, which improves the previous results. As Minieka and Patel observes [sic] (J. Algorithms, Vol. 4, 1983), the problem of finding a core of limited length would be simplified, if the core always contained the median, m. They conclude their paper by writing 'we do not know if a core of length l will contain m. Unfortunately, this situation remains unexplored and as this question remains open, the development of an efficient algorithm for locating a core of a specified length remains a difficult problem.' We show that the median is not necessarily included in the core and give an O(n min [log n[alpha](n, n), l]) algorithm for the problem, which improves the former best result O(n min [n², l log n])(Lo and Peng, J. Algorithms Vol. 20, 1996 and Minieka, Networks Vol, 15, 1985)." Combinatorial optimization Paths and cycles (Graph theory) Trees (Graph theory) Alstrup, Stephen Sonstige oth Datalogisk Institut <København>: DIKU-Rapport 1997,3 (DE-604)BV010011493 1997,3 |
| spellingShingle | Finding cores of limited length Datalogisk Institut <København>: DIKU-Rapport Combinatorial optimization Paths and cycles (Graph theory) Trees (Graph theory) |
| title | Finding cores of limited length |
| title_auth | Finding cores of limited length |
| title_exact_search | Finding cores of limited length |
| title_full | Finding cores of limited length Stephen Alstrup ... |
| title_fullStr | Finding cores of limited length Stephen Alstrup ... |
| title_full_unstemmed | Finding cores of limited length Stephen Alstrup ... |
| title_short | Finding cores of limited length |
| title_sort | finding cores of limited length |
| topic | Combinatorial optimization Paths and cycles (Graph theory) Trees (Graph theory) |
| topic_facet | Combinatorial optimization Paths and cycles (Graph theory) Trees (Graph theory) |
| volume_link | (DE-604)BV010011493 |
| work_keys_str_mv | AT alstrupstephen findingcoresoflimitedlength |