Algorithmica

, Volume 39, Issue 4, pp 321–347 | Cite as

Automated Generation of Search Tree Algorithms for Hard Graph Modification Problems

Article

Abstract

We present a framework for an automated generation of exact search tree algorithms for NP-hard problems. The purpose of our approach is twofold—rapid development and improved upper bounds. Many search tree algorithms for various problems in the literature are based on complicated case distinctions. Our approach may lead to a much simpler process of developing and analyzing these algorithms. Moreover, using the sheer computing power of machines it may also lead to improved upper bounds on search tree sizes (i.e., faster exact solving algorithms) in comparison with previously developed “hand-made” search trees. Among others, such an example is given with the NP-complete Cluster Editing problem (also known as Correlation Clustering on complete unweighted graphs), which asks for the minimum number of edge additions and deletions to create a graph which is a disjoint union of cliques. The hand-made search tree for Cluster Editing had worst-case size O(2.27k), which now is improved to O(1.92k) due to our new method. (Herein, k denotes the number of edge modifications allowed.)

NP-hard problems Graph modification Search tree algorithms Exact algorithms Automated development and analysis of algorithms Algorithm engineering 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany

Personalised recommendations