Engineering Tree Labeling Schemes: A Case Study on Least Common Ancestors

We address the problem of labeling the nodes of a tree such that one can determine the identifier of the least common ancestor of any two nodes by looking only at their labels. This problem has application in routing and in distributed computing in peer-to-peer networks. A labeling scheme using i¾?(log2n)-bit labels has been previously presented by Peleg. By engineering this scheme, we obtain a variety of data structures with the same asymptotic performances. We conduct a thorough experimental evaluation of all these data structures. Our results clearly show which variants achieve the best performances in terms of space usage, construction time, and query time.

[1]  Haim Kaplan,et al.  A comparison of labeling schemes for ancestor queries , 2002, SODA '02.

[2]  Nicolas Bonichon,et al.  Short Labels by Traversal and Jumping , 2006, SIROCCO.

[3]  Philip Bille,et al.  Labeling schemes for small distances in trees , 2003, SODA '03.

[4]  Stephen Alstrup,et al.  Compact Labeling Scheme for Ancestor Queries , 2006, SIAM J. Comput..

[5]  Haim Kaplan,et al.  Compact labeling schemes for ancestor queries , 2001, SODA '01.

[6]  Moshe Lewenstein,et al.  Dynamic weighted ancestors , 2007, SODA '07.

[7]  David Peleg,et al.  Proximity-Preserving Labeling Schemes and Their Applications , 1999, WG.

[8]  Melvin A. Breuer,et al.  An unexpected result in coding the vertices of a graph , 1967 .

[9]  Mogens Nielsen,et al.  Mathematical Foundations of Computer Science 2000 , 2001, Lecture Notes in Computer Science.

[10]  Melvin A. Breuer,et al.  Coding the vertexes of a graph , 1966, IEEE Trans. Inf. Theory.

[11]  Richard Cole,et al.  Dynamic LCA queries on trees , 1999, SODA '99.

[12]  Saverio Caminiti,et al.  On coding labeled trees , 2007, Theor. Comput. Sci..

[13]  Stephen Alstrup,et al.  Nearest common ancestors: a survey and a new distributed algorithm , 2002, SPAA.

[14]  David Peleg.  Informative Labeling Schemes for Graphs , 2000, MFCS.

[15]  Moni Naor,et al.  Implicit Representation of Graphs , 1992, SIAM J. Discret. Math..

[16]  Ran Raz,et al.  Distance labeling in graphs , 2001, SODA '01.

[17]  David Peleg,et al.  Labeling schemes for flow and connectivity , 2002, SODA '02.

[18]  Edith Cohen,et al.  Reachability and distance queries via 2-hop labels , 2002, SODA '02.