LATIN 2004: LATIN 2004: Theoretical Informatics pp 339-348

# A Unified Approach to Coding Labeled Trees

• Saverio Caminiti
• Irene Finocchi
• Rossella Petreschi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)

## Abstract

We consider the problem of coding labeled trees by means of strings of node labels and we present a unified approach based on a reduction of both coding and decoding to integer (radix) sorting. Applying this approach to four well-known codes introduced by Prüfer [18], Neville [17], and Deo and Micikevicius [5], we close some open problems. With respect to coding, our general sequential algorithm requires optimal linear time, thus solving the problem of optimally computing the second code presented by Neville. The algorithm can be parallelized on the EREW PRAM model, so as to work in O(log n) time using O(n) or $$O(n \sqrt{log n})$$ operations, depending on the code.

With respect to decoding, the problem of finding an optimal sequential algorithm for the second Neville code was also open, and our general scheme solves it. Furthermore, in a parallel setting our scheme yields the first efficient decoding algorithms for the codes in [5] and [17].

## Keywords

Parallel Algorithm Decode Algorithm Parallel Setting Node Label Span Tree Problem
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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## Authors and Affiliations

• Saverio Caminiti
• 1
• Irene Finocchi
• 2
• Rossella Petreschi
• 1
1. 1.DSIUniversità degli Studi di Roma “La Sapienza”RomaItaly
2. 2.DISPUniversità degli Studi di Roma “Tor Vergata”RomaItaly