SWAT 2006: Algorithm Theory – SWAT 2006 pp 411-422

# Linear-Time Algorithms for Tree Root Problems

• Maw-Shang Chang
• Ming-Tat Ko
• Hsueh-I Lu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)

## Abstract

Let T be a tree on a set V of nodes. The p-th power T p of T is the graph on V such that any two nodes u and w of V are adjacent in T p if and only if the distance of u and w in T is at most p. Given an n-node m-edge graph G and a positive integer p, the p-th tree root problem asks for a tree T, if any, such that G=T p . Given a graph G, the tree root problem asks for a positive integer p and a tree T, if any, such that G=T p . Kearney and Corneil gave the best previously known algorithms for both problems. Their algorithm for the former (respectively, latter) problem runs in O(n 3) (respectively, O(n 4)) time. In this paper, we give O(n+m)-time algorithms for both problems.

## Keywords

Linear Time Tree Root SIAM Journal Maximal Clique Input Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2006

## Authors and Affiliations

• Maw-Shang Chang
• 1
• Ming-Tat Ko
• 2
• Hsueh-I Lu
• 3
1. 1.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityMing-Shiun, ChiayiTaiwan
2. 2.Institute of Information ScienceAcademia SinicaTaipeiTaiwan
3. 3.Department of Computer Science and Information EngineeringNational Taiwan UniversityTaipeiTaiwan