Polynomial kernels for Proper Interval Completion and related problems
Given a graph G=(V,E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V×V)∖E such that the graph H=(V,E∪F) is a proper interval graph. The Proper Interval Completion problem finds applications in molecular biology and genomic...
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| Vydané v: | Information and computation Ročník 231; s. 89 - 108 |
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01.10.2013
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| Abstract | Given a graph G=(V,E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V×V)∖E such that the graph H=(V,E∪F) is a proper interval graph. The Proper Interval Completion problem finds applications in molecular biology and genomic research. This problem is known to be FPT (Kaplan, Tarjan and Shamir, FOCSʼ94), but no polynomial kernel was known to exist. We settle this question by proving that Proper Interval Completion admits a kernel with O(k3) vertices. Moreover, we prove that a related problem, the so-called Bipartite Chain Deletion problem, admits a kernel with O(k2) vertices, completing a previous result of Guo (ISAACʼ07). |
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| AbstractList | Given a graph G=(V,E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V×V)∖E such that the graph H=(V,E∪F) is a proper interval graph. The Proper Interval Completion problem finds applications in molecular biology and genomic research. This problem is known to be FPT (Kaplan, Tarjan and Shamir, FOCSʼ94), but no polynomial kernel was known to exist. We settle this question by proving that Proper Interval Completion admits a kernel with O(k3) vertices. Moreover, we prove that a related problem, the so-called Bipartite Chain Deletion problem, admits a kernel with O(k2) vertices, completing a previous result of Guo (ISAACʼ07). |
| Author | Perez, Anthony Bessy, Stéphane |
| Author_xml | – sequence: 1 givenname: Stéphane surname: Bessy fullname: Bessy, Stéphane email: bessy@lirmm.fr organization: LIRMM, CNRS – Université Montpellier II, France – sequence: 2 givenname: Anthony surname: Perez fullname: Perez, Anthony email: anthony.perez@univ-orleans.fr organization: LIFO – Université dʼOrléans, France |
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| Cites_doi | 10.1137/070710913 10.1137/0213035 10.1145/1721837.1721848 10.1016/j.dam.2010.07.002 10.1016/j.dam.2003.07.001 10.1016/0020-0190(96)00050-6 10.1016/j.jcss.2009.04.001 10.1016/S0020-0190(00)00004-1 10.1137/S0097539700372216 10.1016/0020-0190(95)00046-F 10.1016/0898-1221(93)90308-I 10.1016/j.cosrev.2010.01.001 10.1137/0602010 10.1137/S0097539796303044 10.1137/S0097539792269095 10.1016/j.dam.2004.01.007 |
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| Keywords | Graph modification problems Proper interval graphs Kernelization algorithms Parameterized complexity |
| Language | English |
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| SubjectTerms | Computer Science Data Structures and Algorithms Graph modification problems Kernelization algorithms Parameterized complexity Proper interval graphs |
| Title | Polynomial kernels for Proper Interval Completion and related problems |
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