Parameterised Enumeration for Modification Problems
Recently, Creignou et al. (Theory Comput. Syst. 2017), introduced the class DelayFPT into parameterised complexity theory in order to capture the notion of efficiently solvable parameterised enumeration problems. In this paper, we propose a framework for parameterised ordered enumeration and will sh...
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| Veröffentlicht in: | Algorithms Jg. 12; H. 9; S. 189 |
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| Abstract | Recently, Creignou et al. (Theory Comput. Syst. 2017), introduced the class DelayFPT into parameterised complexity theory in order to capture the notion of efficiently solvable parameterised enumeration problems. In this paper, we propose a framework for parameterised ordered enumeration and will show how to obtain enumeration algorithms running with an FPT delay in the context of general modification problems. We study these problems considering two different orders of solutions, namely, lexicographic order and order by size. Furthermore, we present two generic algorithmic strategies. The first one is based on the well-known principle of self-reducibility and is used in the context of lexicographic order. The second one shows that the existence of a neighbourhood structure among the solutions implies the existence of an algorithm running with FPT delay which outputs all solutions ordered non-decreasingly by their size. |
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| AbstractList | Recently, Creignou et al. (Theory Comput. Syst. 2017) have introduced the class 1 DelayFPT into parameterised complexity theory in order to capture the notion of efficiently solvable 2 parameterised enumeration problems. In this paper, we propose a framework for parameterised 3 ordered enumeration and will show how to obtain enumeration algorithms running with an FPT delay 4 in the context of general modification problems. We study these problems considering two different 5 orders of solutions, namely, lexicographic order and order by size. Furthermore, we present two 6 generic algorithmic strategies. The first one is based on the well-known principle of self-reducibility 7 and is used in the context of lexicographic order. The second one shows that the existence of a 8 neighbourhood structure among the solutions implies the existence of an algorithm running with 9 FPT delay which outputs all solutions ordered non-decreasingly by their size. 10 Recently, Creignou et al. (Theory Comput. Syst. 2017), introduced the class DelayFPT into parameterised complexity theory in order to capture the notion of efficiently solvable parameterised enumeration problems. In this paper, we propose a framework for parameterised ordered enumeration and will show how to obtain enumeration algorithms running with an FPT delay in the context of general modification problems. We study these problems considering two different orders of solutions, namely, lexicographic order and order by size. Furthermore, we present two generic algorithmic strategies. The first one is based on the well-known principle of self-reducibility and is used in the context of lexicographic order. The second one shows that the existence of a neighbourhood structure among the solutions implies the existence of an algorithm running with FPT delay which outputs all solutions ordered non-decreasingly by their size. |
| Author | Vollmer, Heribert Creignou, Nadia Meier, Arne Olive, Frédéric Müller, Julian-Steffen Ktari, Raïda |
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| Cites_doi | 10.24963/ijcai.2017/81 10.1016/j.jcss.2019.02.004 10.24963/ijcai.2017/159 10.1007/3-540-45655-4_60 10.1016/j.dam.2004.01.007 10.1002/mcda.1603 10.1016/j.jcss.2016.10.007 10.1016/0020-0190(88)90065-8 10.1016/j.tcs.2005.10.004 10.1137/0602010 10.1016/j.artint.2012.03.002 10.1093/bioinformatics/bts423 10.1016/0166-218X(95)00026-N 10.1007/s00453-018-0515-5 10.1016/j.artint.2014.12.001 10.1016/0020-0190(96)00050-6 10.1137/S0097539796303044 10.1007/BF02679443 10.1007/978-3-642-30891-8_15 10.1017/S0956796811000104 10.1016/j.artint.2018.10.002 10.1007/978-3-319-40970-2_4 10.1007/978-3-642-21581-0_11 10.1051/ita/1997310604991 10.1145/800133.804355 10.1007/s00224-016-9702-4 10.1007/s00236-007-0056-x 10.1016/j.polymer.2007.05.018 10.1590/S0101-74382005000200004 10.1145/2818646 10.1007/s00453-003-1028-3 10.1137/12089051X |
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| SubjectTerms | Algorithms Artificial Intelligence bounded search tree Complexity theory Computational Complexity Computer Science Context Discrete Mathematics Enumeration Logic in Computer Science ordering parameterised complexity parameterised enumeration Parameterization |
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