"Interesting" Paths = Shortest Paths? - - PowerPoint PPT Presentation

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"Interesting" Paths = Shortest Paths? - - PowerPoint PPT Presentation

Sep 26, 2023 248 likes •788 views

WiSP : Weighted Shortest Paths for RDF graphs Gonzalo Tartari, Aidan Hogan DCC, Universidad de Chile "Interesting" Paths = Shortest Paths? "Interesting" Paths Shortest Paths! (Many of the) Existing Approaches Enumerate

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WiSP:

Weighted Shortest Paths for RDF graphs

Gonzalo Tartari, Aidan Hogan

DCC, Universidad de Chile

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"Interesting" Paths = Shortest Paths?

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"Interesting" Paths ≠ Shortest Paths!

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Output

(Many of the) Existing Approaches

Enumerate Paths Score Paths Order/Filter Paths

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Enumerate Paths Output

(Many of the) Existing Approaches

Score Paths Order/Filter Paths Enumerate Paths

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Output

(Many of the) Existing Approaches

Score Paths Order/Filter Paths Enumerate Paths

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Our Approach: Weight Graphs

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Wei eigh ghti ting ng gr graphs hs: No Node des

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Node Weights: Length (Baseline)

...

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Node Weights: Degree

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Node Weights: PageRank

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Aside: PageRank / directed graph used

...

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Wei eigh ghti ting ng gr graphs hs: Ed Edge ges

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Weighting with only nodes

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Weighting with only nodes

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Edge Weights: Frequency

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Wei eigh ghti ting ng gr graphs hs: No Node des + E s + Edg dges es

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Node + Edge Weights: Degree + Frequency

...

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Node + Edge Weights: PageRank + Frequency

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Node + Edge Weights: PageRank + Frequency

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Node + Edge Weights: [0,1] Normalisation

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Hy Hybrid d No Node de Wei eigh ghts ts

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Node Weights: PageRank

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Visiting one high-centrality node = Visiting thousands of low-centrality nodes

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Hybrid Node Weights: PageRank + Length

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Imp mplem emen entat tation

  • n
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Weighted Shortest-Path Implementation

  • Dijsktra's algorithm:

– Worst case:

Image source: https://github.com/aakash1104/Graph-Algorithms

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Ex Exper erimen ments ts

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Questions

  • Performance:

– How are the runtimes? – How is the scalability?

  • Weighting schemes:

– How similar are paths for different weightings? – Does weighting help find interesting paths? – Which weighting finds the most interesting paths?

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Dataset: Wikidata

  • Truthy dump: 2017-06-07

– 25 million nodes ( -IRIs only) – 90 million edges

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Dataset: Wikidata Slices

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Machine

  • 2 x Intel Xeon Quad Core @1.9GHz
  • 32 GB of RAM
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Weighting Schemes

  • Node

– Degree ( ) – PageRank ( ) – Length ( )

  • Node + Edge

– Degree + Edge Frequency ( ) – PageRank + Edge Frequency ( )

  • Hybrid Node + Edge

– Degree + Length + Edge Frequency ( ) – PageRank + Length + Edge Frequency ( )

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Pe Perfo forma manc nce

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Queries (Node pairs)

  • Queries: 100 node pairs randomly sampled

– From smallest slice ( code < ) – From each slice independently

  • Task: Return one (best) path
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Performance Results (Full Dataset)

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Performance Results ( | Various Scales)

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Comp mpariso ison n of w f wei eigh ghti ting ng sc sche heme mes

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Comparison of path length (full dataset)

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How many pairs give the same path? (full dataset)

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Us User er Stu tudy dy

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Queries: Same type

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Queries: Different types

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User study

  • 10 students
  • 1.6 M dataset
  • Shown all paths for one query together
  • Scores: 1 (very poor) - 7 (very good)
  • 79 complete evaluations

– 4 evaluations per query (node pair) – 553 scores

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Lowest-rated path

mean score 1.25 ( {1,1,1,2} )

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Highest-rated path

mean score 6.0 ( {5,7} )

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Inter-rater agreement

  • Kendall's τ correlation (ordinal scales)

– τ = 0.201 – Slight, positive agreement

  • Two sets of results

– All

  • τ = 0.201, 20 queries, 79 evaluations

– Concordant

  • Queries with positive τ correlation only
  • τ = 0.552, 8 queries, 27 evaluations
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User study: Comparison of weightings

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Dem emo

http://wisp.dcc.uchile.cl

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WiSP Demo

?

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Conc nclus lusion

  • ns
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Conclusions

  • Performance:

– How are the runtimes?

  • A few seconds (1.6 m) to a few minutes (full dataset)

– How is the scalability?

  • Linear (roughly)
  • Weighting schemes:

– How similar are paths for different weightings?

  • |

similar; others not so much

– Does weighting help find interesting paths?

  • Yes!

– Which weighting finds the most interesting paths?

  • No clear winner (

best in most cases)

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Future work

  • Top-k queries
  • Explore more weightings
  • Normalisation / combinations
  • Performance? (Parallelism? Approximation?)
  • ¡¡¡Evaluation!!!