2013/09/19 by Nadia Creignou, Raïda Ktari, Creignou, Nadia +9
Computer Science · #Advanced Graph Theory Research #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #F.1.3 #FOS: Computer and information sciences #Formal Methods in Verification #cs.CC #cs.DS #msc:F.1.3 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1309.5009
15 pages
openalex publication_date 2013/09/19 · arxiv created 2013/10/07 · arxiv updated 2013/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classes Delay-FPT and Total-FPT recently have been introduced into parameterized complexity in order to capture the notion of efficiently solvable parameterized enumeration problems. In this paper we focus on ordered enumeration and will show how to obtain Delay-FPT and Total-FPT enumeration algorithms for several important problems. We propose a generic algorithmic strategy, combining well-known principles stemming from both parameterized algorithmics and enumeration, which shows that, under certain preconditions, the existence of a so-called neighbourhood function among the solutions implies the existence of a Delay-FPT algorithm which outputs all ordered solutions. In many cases, the cornerstone to obtain such a neighbourhood function is a Total-FPT algorithm that outputs all minimal solutions. This strategy is formalized in the context of graph modification problems, and shown to be applicable to numerous other kinds of problems.