On coding labeled trees

Caminiti, Saverio; Finocchi, Irene; Petreschi, Rossella

doi:10.1016/j.tcs.2007.03.009

Cited by 19 publications

(20 citation statements)

References 9 publications

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“…As usual in mathematics, we use square brackets to include one or both endpoints. As an example, P (3,6] represents the set {0, 2, 6, 8} in the digraph of Figure 1a.…”

Section: Lemma 1 a Digraph G = (V E) Is A Functional Digraph If Andmentioning

confidence: 99%

“…Encoding and decoding in sequential linear time is possible for all bijective codes presented in this introduction (see [5] for Prüfer-like codes, see [6] for Dandelion-like codes and [4] for a survey). Concerning parallel algorithms, studies have been performed and algorithms are known both for Prüfer-like codes [5] and for Dandelion-like codes [7].…”

Section: Introductionmentioning

confidence: 99%

“…Concerning parallel algorithms, studies have been performed and algorithms are known both for Prüfer-like codes [5] and for Dandelion-like codes [7]. The interested reader may found a complete survey on all these codes in [3].…”

Section: Introductionmentioning

confidence: 99%

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Parallel Algorithms for Encoding and Decoding Blob Code

Caminiti

Petreschi

2010

WALCOM: Algorithms and Computation

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Abstract. A bijective code is a method for associating labeled n-trees to (n − 2)-strings of node labels in such a way that different trees yield different strings and vice versa. For all known bijective codes, optimal sequential encoding and decoding algorithms are presented in literature, while parallel algorithms are investigated only for some of these codes. In this paper we focus our attention on the Blob code: a code particularly considered in the field of Genetic Algorithms. To the best of our knowledge, here we present the first parallel encoding and decoding algorithms for this code. The encoding algorithm implementation is optimal on an EREW PRAM, while the decoding algorithm requires O(log n) time and O(n) processors on CREW PRAM.

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“…As usual in mathematics, we use square brackets to include one or both endpoints. As an example, P (3,6] represents the set {0, 2, 6, 8} in the digraph of Figure 1a.…”

Section: Lemma 1 a Digraph G = (V E) Is A Functional Digraph If Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parallel Algorithms for Encoding and Decoding Blob Code

Caminiti

Petreschi

2010

WALCOM: Algorithms and Computation

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“…In particular we refer to [15] for the class of Prüfer-like codes (the first 4 codes in Table 1) Work partially supported by Sapienza University of Rome under the project "Strutture Dati e Tecniche Algoritmiche Evolute per Modelli di Calcolo Innovativi". Table 1.…”

Section: Introductionmentioning

confidence: 99%

Parallel Algorithms for Dandelion-Like Codes

Caminiti

Petreschi

2009

Lecture Notes in Computer Science

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Abstract. We consider the class of Dandelion-like codes, i.e., a class of bijective codes for coding labeled trees by means of strings of node labels. In the literature it is possible to find optimal sequential algorithms for codes belonging to this class, but, for the best of our knowledge, no parallel algorithm is reported. In this paper we present the first encoding and decoding parallel algorithms for Dandelion-like codes. Namely, we design a unique encoding algorithm and a unique decoding algorithm that, properly parametrized, can be used for all Dandelion-like codes. These algorithms are optimal in the sequential setting. The encoding algorithm implementation on an EREW PRAM is optimal, while the efficient implementation of the decoding algorithm requires concurrent reading.

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“…Indeed, many other known codes for Cayley's trees, such as Prüfer-like codes [5], can be generalized to code edge labeled trees, obtaining bijection between Rényi k-trees and strings in B n,k . However these codes do not make it possible to identify a removable redundant pair.…”

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confidence: 99%

Bijective Linear Time Coding and Decoding for k-Trees

2008

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Abstract. The problem of coding labeled trees has been widely studied in the literature and several bijective codes that realize associations between labeled trees and sequences of labels have been presented. k-trees are one of the most natural and interesting generalizations of trees and there is considerable interest in developing efficient tools to manipulate this class of graphs, since many NP-Complete problems have been shown to be polynomially solvable on k-trees and partial k-trees. In 1970 Rényi and Rényi generalized the Prüfer code, the first bijective code for trees, to a subset of labeled k-trees. Subsequently, non redundant codes that realize bijection between k-trees (or Rényi k-trees) and a well defined set of strings were produced. In this paper we introduce a new bijective code for labeled k-trees which, to the best of our knowledge, produces the first coding and decoding algorithms running in linear time with respect to the size of the k-tree.

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On coding labeled trees

Cited by 19 publications

References 9 publications

Parallel Algorithms for Encoding and Decoding Blob Code

Parallel Algorithms for Encoding and Decoding Blob Code

Parallel Algorithms for Dandelion-Like Codes

Bijective Linear Time Coding and Decoding for k-Trees

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