This document presents an algorithm called CORE for generating compact yet relaxable answers to keyword queries over knowledge graphs. CORE aims to balance answer compactness, defined as having a bounded diameter, with answer completeness, defined as covering the most query keywords. It provides theoretical foundations for the existence of such answers and uses a best-first search approach. An evaluation shows CORE efficiently computes answers that are more complete than alternatives while remaining compact.

1. Generating Compact and Relaxable Answers to
Keyword Queries over Knowledge Graphs
Gong Cheng1, Shuxin Li1, Ke Zhang1, Chengkai Li2
1State Key Laboratory for Novel Software Technology, Nanjing University, China
2Department of Computer Science and Engineering, University of Texas at Arlington, United States
ISWC 2020 1

2. ISWC 2020 2
Keyword Search over Knowledge Graphs
United States (US)
United Kindom (UK)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
BBC
headquarters
Yellowstone (YS) The Trip (TT)
Q: united states yellowstone park trip
Ohio
country
London
country
producedBy
G7
member
member
producedBy
country
G

3.  Two Paradigms
 For lookup tasks: semantic parsing (keyword query  SPARQL query)
ISWC 2020 3
Keyword Search over Knowledge Graphs
United States (US)
United Kindom (UK)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
BBC
headquarters
Yellowstone (YS) The Trip (TT)
Q: united states yellowstone park trip
Ohio
country
London
country
producedBy
G7
member
member
producedBy
country
G

4.  Two Paradigms
 For lookup tasks: semantic parsing (keyword query  SPARQL query)
 For exploratory tasks: answer subgraph extraction (keyword query  GST)
ISWC 2020 4
Keyword Search over Knowledge Graphs
United States (US)
United Kindom (UK)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
BBC
headquarters
Yellowstone (YS) The Trip (TT)
Q: united states yellowstone park trip
Ohio
country
London
country
producedBy
G7
member
member
producedBy
countryGroup Steiner Tree
(GST)

5.  Answer completeness?
 Covering all the query keywords
 Answer compactness?
 Having a compact structure (e.g., a small diameter)
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Motivation --- Pros and Cons of GST
Group Steiner Tree
(GST)
United States (US)
United Kindom (UK)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
BBC
headquarters
The Trip (TT)
country
London
country
producedBy
G7
member
member
diameter: 7
uncovered keywords: 0

6.  Computing compact but relaxable subgraphs
 Guaranteed answer compactness: having a bounded diameter (D)
 Maximized answer completeness: covering the largest number of query
keywords
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Main Idea
Group Steiner Tree
(GST)
United States (US)
United Kindom (UK)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
BBC
headquarters
The Trip (TT)
country
London
country
producedBy
G7
member
member
diameter: 7
uncovered keywords: 0

7.  Computing compact but relaxable subgraphs
 Guaranteed answer compactness: having a bounded diameter (D)
 Maximized answer completeness: covering the largest number of query
keywords
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Main Idea
Minimally Relaxed Answer
(MRA)
United States (US)
United Kindom (UK)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
BBC
headquarters
The Trip (TT)
country
London
country
producedBy
G7
member
member
diameter: 2
uncovered keywords: 1
(D=2)

8.  A necessary and sufficient condition for the existence of a
compactness-bounded complete answer to a keyword query
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Approach --- Theoretical Foundations
United States (US)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
country
We refer to v as a certificate vertex for Q.
• E.g., Montana for "united states yellowstone park" under D=2

9. ISWC 2020 9
Approach --- Algorithm CORE
 A best-first search algorithm
one independent search
starting from each
keyword vertex
a shared priority queue keeping
search frontiers
(priority: potentially uncovered
keywords, based on distances)
a more complete answer
which the current vertex
is a certificate vertex for
early stop
unvisited neighbors

10.  Running example
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Approach --- Algorithm CORE
United States (US)
United Kindom (UK)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
BBC
headquarters
Yellowstone (YS) The Trip (TT)
Q: united states yellowstone park trip
Ohio
country
London
country
producedBy
G7
member
member
producedBy
country
G

11.  Running example
ISWC 2020 11
Approach --- Algorithm CORE
United States (US)
United Kindom (UK)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
BBC
headquarters
Yellowstone (YS) The Trip (TT)
Q: united states yellowstone park trip
Ohio
country
London
country
producedBy
G7
member
member
producedBy
country
G

12.  Running example
ISWC 2020 12
Approach --- Algorithm CORE
United States (US)
United Kindom (UK)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
BBC
headquarters
Yellowstone (YS) The Trip (TT)
Q: united states yellowstone park trip
Ohio
country
London
country
producedBy
G7
member
member
producedBy
country
G

13.  Running example
ISWC 2020 13
Approach --- Algorithm CORE
United States (US)
United Kindom (UK)
Montana (MT)
Yellowstone National
Park (YSNP)
isLocatedIn
BBC
headquarters
Yellowstone (YS) The Trip (TT)
Q: united states yellowstone park trip
Ohio
country
London
country
producedBy
G7
member
member
producedBy
country
G

14.  Datasets
 Baselines
 CertQR+ (adapted to our problem)
 GST-based answers
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Experiment Settings

15.  Main finding
 Trading off answer completeness for compactness is necessary.
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Results --- Compactness of GST-Based Answers
(doc = diameter; |K| = max keyword hits)

16.  Main finding
 The completeness of our computed answers is very high.
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Results --- Completeness of Relaxable Answers
(dor = number of uncovered keywords; |K| = max keyword hits)

17.  Main finding
 CORE is efficient and significantly outperforms CertQR+.
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Results --- Efficiency of CORE

18.  Take-home messages
 Necessity of trading off answer completeness for compactness
 Polynomial-time algorithm for generating compact but relaxable answers
 https://github.com/nju-websoft/CORE
 Future work
 Vertex and/or edge weights
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Conclusion