Skolemising Blank Nodes while Preserving Isomorphism
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The document discusses the importance and challenges of blank nodes in RDF graphs, emphasizing their common usage in real-world data to simplify syntax and specify complex relationships. It critiques the existing methods of skolemisation for preserving isomorphism and proposes a complete yet efficient canonical labeling scheme to distinguish blank nodes. The evaluation of this method considers both real-world and synthetic graph scenarios, highlighting the need for optimization in graph-level hashing to manage automorphisms and reduce complexity.
Skolemising Blank Nodes while Preserving Isomorphism
- 1. Skolemising Blank Nodes while Preserving Isomorphism Aidan Hogan – DCC, Universidad de Chile
- 2. WHY? BLANK NODES ARE GREAT!
- 3. When life gives you blank nodes …
- 4. Blank Nodes are glue!
- 5. Blank Nodes names aren’t important … (Isomorphic)
- 6. Blank nodes are common in real-world data … Aidan Hogan, Marcelo Arenas, Alejandro Mallea and Axel Polleres "Everything You Always Wanted to Know About Blank Nodes". Journal of Web Semantics 27: pp. 42–69, 2014
- 7. BLANK NODES ENABLE SYNTAX SHORTCUTS They represent implicit nodes in the graph They help specify order, higher-arity relations, reification, etc., succinctly They are common in real-world data
- 8. BLANK NODES: WHAT’S THE PROBLEM?
- 9. Are two RDF graphs isomorphic?
- 10. Are two RDF graphs isomorphic?
- 11. RDF ISOMORPHISM IS GI-COMPLETE A general algorithm to see if two RDF graphs are the “same” will (probably) not be tractable
- 12. BLANK NODES ADD COMPLEXITY? WHAT TO DO?
- 13. RDF 1.1 proposes Skolemisation
- 14. But fresh IRIs every time is not ideal
- 15. But fresh IRIs every time is not ideal
- 16. Would prefer a “consistent” labelling
- 17. Would prefer a “consistent” labelling
- 18. Compute isomorphically-unique graph hash
- 19. Finding duplicate documents from a crawler
- 20. CANONICAL LABELLING USEFUL FOR: 1. Mapping blank nodes to IRIs 2. Computing unique hashes for RDF graphs
- 21. OLD BUT RECURRING QUESTION
- 22. An old question that won’t go away … Jeremy J. Carroll. “Signing RDF Graphs.” ISWC 2003. Edzard Höfig, Ina Schieferdecker. “Hashing of RDF Graphs and a Solution to the Blank Node Problem.” URSW 2014.
- 23. NO EXISTING APPROACH IS GENERAL • Hard cases seem unlikely in practice • Let’s build a general (and thus worst-case exponential) algorithm that’s efficient for practical cases
- 24. NAÏVE CANONICAL LABELLING SCHEME
- 25. (Naïve) Canonical labels for blank nodes
- 26. But wait … what happens if ... ?
- 27. Or another case …
- 28. Or another case …
- 29. Or another case …
- 30. Fixpoint does not distinguish all blank nodes!
- 31. NAÏVE: COLOUR BLANK NODES RECURSIVELY UNTIL FIXPOINT • Efficient • Incomplete
- 32. CANONICAL LABELLING SCHEME: ALWAYS DISTINGUISH ALL BLANK NODES Brendan D. McKay. "Practical graph isomorphism". Congressus Numerantium 30: pp. 45–87, 1981.
- 33. Start with a (non-distinguished) colouring …
- 34. Let’s distinguish a node …
- 35. Let’s distinguish a node …
- 36. Colouring is no longer a fixpoint!
- 37. Rerun colouring to fixpoint
- 38. Rerun colouring to fixpoint
- 39. Rerun colouring to fixpoint
- 40. Rerun colouring to fixpoint
- 41. Fixpoint reached: still not finished!
- 42. So again let’s distinguish another …
- 43. … and rerun colouring to fixpoint
- 44. … and rerun colouring to fixpoint
- 45. … and rerun colouring to fixpoint
- 46. … and rerun colouring to fixpoint
- 47. … and rerun colouring to fixpoint
- 48. … and rerun colouring to fixpoint
- 49. Now all blank nodes are distinguished!
- 50. Blank node labels computed from colour
- 51. Let’s go back: first, why pick _:a and _:c?
- 52. Okay so: why _:a …
- 53. Adapt ideas from the Nauty algorithm (for standard graph isomorphism)
- 54. Adapt ideas from the Nauty algorithm (for standard graph isomorphism)
- 55. Check all leafs for minimum graph
- 56. What happened?
- 57. What happened?
- 58. What happened?
- 60. CORE ALGORITHM: FIND MINIMAL GRAPH FOLLOWING FIXED COLOURING RULES • Complete • Efficient for many cases?
- 61. OKAY … SO WHAT HASHING TO USE?
- 62. What about hash collisions? 128 bit: MD5, Murmur3_128 160 bit: SHA1
- 63. HASHING MAY LEAD TO COLLISIONS • Don’t care what hashing you want to use • 128-bit hash shortest hash with acceptable collision probability • For cryptographic use-cases, SHA-256 or better might be needed
- 64. EVALUATION
- 66. Evaluation: Nasty Synthetic Graphs
- 67. CONCLUSIONS
- 68. In loving memory of Linked Data 2007–2012 Survived by its research community _:b 1999–2015
- 69. Conclusions
- 71. Aside: Why GI-Hard? (Can Encode Graph Isomorphism as RDF Isomorphism) if and only if
- 72. Aside: Why GI-Complete? (Can we encode RDF isomorphism as graph isomorphism?) if and only if ? ?
- 73. Aside: Why GI-Complete? (Yes: We can encode RDF isomorphism as graph isomorphism)
- 74. Aside: Why GI-Complete? (Yes: We can encode RDF isomorphism as graph isomorphism) if and only if
- 75. COMPLETE CANONICAL LABELLING SCHEME
- 76. A complete canonical labelling?
- 77. Find a canonical labelling for H
- 78. Choose the lowest possible graph
- 79. COMPLETE: FIND MINIMUM POSSIBLE GRAPH USING FIXED BLANK NODE LABELS • Complete • Inefficient
- 80. The need for a graph-level hash
- 81. OPTIMISATION: PRUNE THE TREE USING AUTOMORPHISMS
- 82. Trim the search tree using “found” automorphisms Found Automorphisms …
- 83. PRUNING PER AUTOMORPHISMS AVOIDS SYMMETRIC REPETITIONS • Automorphisms are found naturally • Makes very “regular” structures (like cliques) a lot easier • Need to be careful how to manage the automorphism group