Automated Search Tree Generation
Years and Authors of Summarized Original Work
2004; Gramm, Guo, Hüffner, Niedermeier
This problem is concerned with the automated development and analysis of search tree algorithms. Search tree algorithms are a popular way to find optimal solutions to NP-complete problems.1 The idea is to recursively solve several smaller instances in such a way that at least one branch is a yes-instance if and only if the original instance is. Typically, this is done by trying all possibilities to contribute to a solution certificate for a small part of the input, yielding a small local modification of the instance in each branch.
For example, consider the NP-complete Cluster Editing problem: can a given graph be modified by adding or deleting up to k edges such that the resulting graph is a cluster graph, that is, a graph that is a disjoint union of cliques? To give a search tree algorithm for Cluster Editing, one can use the fact that cluster graphs are exactly the graphs that do...
KeywordsAutomated proofs of upper bounds on the running time of splitting algorithms
Partially supported by the Deutsche Forschungsgemeinschaft, Emmy Noether research group PIAF (fixed‐parameter algorithms), NI 369/4.
- 1.Eppstein D (2004) Quasiconvex analysis of backtracking algorithms. In: Proceedings of the 15th SODA. ACM/SIAM, pp 788–797Google Scholar
- 5.Hüffner F (2003) Graph modification problems and automated search tree generation. Diplomarbeit, Wilhelm-Schickard-Institut für Informatik, Universitüt TübingenGoogle Scholar
- 6.Skjernaa B (2004) Exact algorithms for variants of satisfiability and colouring problems. PhD thesis, Department of Computer Science, University of AarhusGoogle Scholar