On the complexity of computing evolutionary trees
In this paper we study a few important tree optimization problems with applications to computational biology. These problems ask for trees that are consistent with an as large part, of the given data as possible. We show that the maximum homeomorphic agreement subtree problem cannot be approximated...
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| creator | Gasieniec, Leszek Jansson, Jesper Lingas, Andrzej Östlin, Anna |
| description | In this paper we study a few important tree optimization problems with applications to computational biology. These problems ask for trees that are consistent with an as large part, of the given data as possible. We show that the maximum homeomorphic agreement subtree problem cannot be approximated within a factor of Nε, where N is the input size, for any 0 ≤ ε < 1/18 in polynomial time unless P=NP, even if all the given trees are of height 2. On the other hand, we present an O(N log N)-time heuristic for the restriction of this problem to instances with O(1) trees of height O(1) yielding solutions within a constant factor of the optimum. We prove that the maximum inferred consensus tree problem is NP-complete, and we provide a simple fast heuristic for it yielding solutions within one third of the optimum. We also present a more specialized polynomial-time heuristic for the maximum inferred local consensus tree problem. |
| doi_str_mv | 10.1007/BFb0045080 |
| format | Book Chapter |
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On the other hand, we present an O(N log N)-time heuristic for the restriction of this problem to instances with O(1) trees of height O(1) yielding solutions within a constant factor of the optimum. We prove that the maximum inferred consensus tree problem is NP-complete, and we provide a simple fast heuristic for it yielding solutions within one third of the optimum. We also present a more specialized polynomial-time heuristic for the maximum inferred local consensus tree problem.</description><subject>Applied sciences</subject><subject>Artificial intelligence</subject><subject>Biological and medical sciences</subject><subject>Computer science; control theory; systems</subject><subject>Consensus Tree</subject><subject>Exact sciences and technology</subject><subject>Fundamental and applied biological sciences. Psychology</subject><subject>General aspects</subject><subject>Greedy Method</subject><subject>Input Constraint</subject><subject>Mathematics in biology. Statistical analysis. 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Data processing in biology (general aspects)</subject><subject>Polynomial Time</subject><subject>Priority Queue</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540633570</isbn><isbn>354063357X</isbn><isbn>9783540695226</isbn><isbn>3540695222</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2006</creationdate><recordtype>book_chapter</recordtype><recordid>eNpFkEtPwzAQhM1LIpRe-AU5cOASWO86fhyhooBUqRc4W05ql0CaRHFA7b8nUKSedlbzabUzjF1xuOUA6u5hXgCIHDQcsalRmnIB0uSI8pglXHKeEQlzcvCIcgWnLAECzIwSdM4uYvwAAFQGE8aXTTq8-7RsN13tt9WwS9vwt30NVbNO_Xdbj6ptXL9Lh977eMnOgqujn_7PCXubP77OnrPF8ulldr_IOi41ZNxzLqVAxYtSUiGIaEVOYUDMFZL0AEE5qYyXzq9KjUF4EzRKgwYLvaIJu97f7VwsXR1615RVtF1fbcZfLKoxKOgRu9ljcXSate9t0baf0XKwv43ZQ2P0A2NgVtU</recordid><startdate>20060124</startdate><enddate>20060124</enddate><creator>Gasieniec, Leszek</creator><creator>Jansson, Jesper</creator><creator>Lingas, Andrzej</creator><creator>Östlin, Anna</creator><general>Springer Berlin Heidelberg</general><general>Springer-Verlag</general><scope>IQODW</scope></search><sort><creationdate>20060124</creationdate><title>On the complexity of computing evolutionary trees</title><author>Gasieniec, Leszek ; Jansson, Jesper ; Lingas, Andrzej ; Östlin, Anna</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p1680-1e11664271bc63b4333d3a72f2257236e00f7a679e6aedc82f4e9f8269292b8d3</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Biological and medical sciences</topic><topic>Computer science; control theory; systems</topic><topic>Consensus Tree</topic><topic>Exact sciences and technology</topic><topic>Fundamental and applied biological sciences. Psychology</topic><topic>General aspects</topic><topic>Greedy Method</topic><topic>Input Constraint</topic><topic>Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)</topic><topic>Polynomial Time</topic><topic>Priority Queue</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gasieniec, Leszek</creatorcontrib><creatorcontrib>Jansson, Jesper</creatorcontrib><creatorcontrib>Lingas, Andrzej</creatorcontrib><creatorcontrib>Östlin, Anna</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gasieniec, Leszek</au><au>Jansson, Jesper</au><au>Lingas, Andrzej</au><au>Östlin, Anna</au><au>Lee, D. 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| ispartof | Computing and Combinatorics, 2006, p.134-145 |
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| language | eng |
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| source | Springer Books |
| subjects | Applied sciences Artificial intelligence Biological and medical sciences Computer science control theory systems Consensus Tree Exact sciences and technology Fundamental and applied biological sciences. Psychology General aspects Greedy Method Input Constraint Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects) Polynomial Time Priority Queue |
| title | On the complexity of computing evolutionary trees |
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