Automated Search Tree Generation
Keywords and Synonyms
Automated proofs of upper bounds on the running time of splitting algorithms
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...
KeywordsVertex Cover Editing Operation Cluster Graph Polynomial Factor Original Instance
Partially supported by the Deutsche Forschungsgemeinschaft, Emmy Noether research group PIAF (fixed‐parameter algorithms), NI 369/4.
- 1.Eppstein, D.: Quasiconvex analysis of backtracking algorithms. In: Proc. 15th SODA, ACM/SIAM, pp. 788–797 (2004)Google Scholar
- 5.Hüffner, F.: Graph Modification Problems and Automated Search Tree Generation. Diplomarbeit, Wilhelm‐Schickard‐Institut für Informatik, Universität Tübingen (2003)Google Scholar
- 6.Skjernaa, B.: Exact Algorithms for Variants of Satisfiability and Colouring Problems. Ph. D. thesis, University of Aarhus, Department of Computer Science (2004)Google Scholar