On Compact Encoding of Pagenumber $k$ Graphs
In this paper we show an information-theoretic lower bound of kn - o(kn) on the minimum number of bits to represent an unlabeled simple connected n-node graph of pagenumber k. This has to be compared with the efficient encoding scheme of Munro and Raman of 2kn + 2m + o(kn+m) bits (m the number of ed...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2008-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/436/pdf |
| _version_ | 1827323874085175296 |
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| author | Cyril Gavoille Nicolas Hanusse |
| author_facet | Cyril Gavoille Nicolas Hanusse |
| author_sort | Cyril Gavoille |
| collection | DOAJ |
| description | In this paper we show an information-theoretic lower bound of kn - o(kn) on the minimum number of bits to represent an unlabeled simple connected n-node graph of pagenumber k. This has to be compared with the efficient encoding scheme of Munro and Raman of 2kn + 2m + o(kn+m) bits (m the number of edges), that is 4kn + 2n + o(kn) bits in the worst-case. For m-edge graphs of pagenumber k (with multi-edges and loops), we propose a 2mlog2k + O(m) bits encoding improving the best previous upper bound of Munro and Raman whenever m ≤ 1 / 2kn/log2 k. Actually our scheme applies to k-page embedding containing multi-edge and loops. Moreover, with an auxiliary table of o(m log k) bits, our coding supports (1) the computation of the degree of a node in constant time, (2) adjacency queries with O(logk) queries of type rank, select and match, that is in O(logk *minlogk / loglogm, loglogk) time and (3) the access to δ neighbors in O(δ) runs of select, rank or match;. |
| first_indexed | 2024-04-25T01:59:39Z |
| format | Article |
| id | doaj.art-8027c3fb13d44f37ba793ae61fd7f30c |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:59:39Z |
| publishDate | 2008-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-8027c3fb13d44f37ba793ae61fd7f30c2024-03-07T15:12:27ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502008-01-01Vol. 10 no. 310.46298/dmtcs.436436On Compact Encoding of Pagenumber $k$ GraphsCyril Gavoille0https://orcid.org/0000-0003-3671-8607Nicolas Hanusse1Algorithmics for computationally intensive applications over wide scale distributed platformsAlgorithmics for computationally intensive applications over wide scale distributed platformsIn this paper we show an information-theoretic lower bound of kn - o(kn) on the minimum number of bits to represent an unlabeled simple connected n-node graph of pagenumber k. This has to be compared with the efficient encoding scheme of Munro and Raman of 2kn + 2m + o(kn+m) bits (m the number of edges), that is 4kn + 2n + o(kn) bits in the worst-case. For m-edge graphs of pagenumber k (with multi-edges and loops), we propose a 2mlog2k + O(m) bits encoding improving the best previous upper bound of Munro and Raman whenever m ≤ 1 / 2kn/log2 k. Actually our scheme applies to k-page embedding containing multi-edge and loops. Moreover, with an auxiliary table of o(m log k) bits, our coding supports (1) the computation of the degree of a node in constant time, (2) adjacency queries with O(logk) queries of type rank, select and match, that is in O(logk *minlogk / loglogm, loglogk) time and (3) the access to δ neighbors in O(δ) runs of select, rank or match;.https://dmtcs.episciences.org/436/pdf[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Cyril Gavoille Nicolas Hanusse On Compact Encoding of Pagenumber $k$ Graphs Discrete Mathematics & Theoretical Computer Science [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | On Compact Encoding of Pagenumber $k$ Graphs |
| title_full | On Compact Encoding of Pagenumber $k$ Graphs |
| title_fullStr | On Compact Encoding of Pagenumber $k$ Graphs |
| title_full_unstemmed | On Compact Encoding of Pagenumber $k$ Graphs |
| title_short | On Compact Encoding of Pagenumber $k$ Graphs |
| title_sort | on compact encoding of pagenumber k graphs |
| topic | [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/436/pdf |
| work_keys_str_mv | AT cyrilgavoille oncompactencodingofpagenumberkgraphs AT nicolashanusse oncompactencodingofpagenumberkgraphs |