1 research outputs found
μλ³ μ κ°μ κ³Ό ν¨μ¨μ μΈ λ°±νΈλνΉμ μ΄μ©ν λΉ λ₯Έ κ·Έλν λν μκ³ λ¦¬μ¦
νμλ
Όλ¬Έ(λ°μ¬) -- μμΈλνκ΅λνμ : 곡과λν μ»΄ν¨ν°κ³΅νλΆ, 2021.8. ꡬ건λͺ¨.Graph isomorphism is a core problem in graph analysis of various domains including social networks, bioinformatics, chemistry, and so on. As real-world graphs are getting bigger and bigger, applications demand practically fast algorithms that can run on large-scale graphs. Existing approaches, however, show limited performances on large-scale real-world graphs either in time or space. Also, graph isomorphism query processing is often required in many applications, which is a natural generalization of graph isomorphism for multiple graphs. In this thesis we present fast algorithms for graph isomorphism and graph isomorphism query processing.
First, we present a new approach to graph isomorphism, which is the framework of pairwise color refinement and efficient backtracking. Within the framework, we introduce three efficient techniques, which together lead to a much faster and scalable algorithm for graph isomorphism. Experiments on real-world datasets show that our algorithm outperforms state-of-the-art solutions by up to several orders of magnitude in terms of running time.
Second, We develop an efficient algorithm for graph isomorphism query processing. We use a two-level index using degree sequences and color-label distributions. Experimental results on real datasets show that our algorithm is orders of magnitude faster than the state-of-the-art algorithms in terms of index construction time, and it runs faster than existing algorithms in terms of query processing time as the graph sizes increase.κ·Έλν λν λ¬Έμ λ μμ
λ€νΈμν¬ μλΉμ€, μλ¬Όμ 보ν, ννμ 보ν λ±λ± λ€μν μμ© λΆμΌμμ κ·Έλν λΆμμ μν΄ λ€λ£¨κ³ μλ ν΅μ¬ λ¬Έμ μ΄λ€. μ€μνμμ λ€λ£¨λ κ·Έλν λ°μ΄ν°μ ν¬κΈ°κ° μ»€μ Έ κ°μ λ°λΌ, λμ©λμ κ·Έλνλ₯Ό μ²λ¦¬ν μ μλ κ·Έλν λν μκ³ λ¦¬μ¦μ νμμ±μ΄ λμμ§κ³ μλ€. κ·Έλ¬λ νμ¬ μ‘΄μ¬νλ κ·Έλν λν μκ³ λ¦¬μ¦λ€μ λμ©λμ κ·Έλνμ λν΄μ μκ° νΉμ κ³΅κ° μΈ‘λ©΄μμ νκ³λ₯Ό 보μ¬μ€λ€. μμ© λΆμΌ μ€μμλ μ¬λ¬ κ°μ κ·Έλνλ€ μ€μμ νλμ 쿼리 κ·Έλνμ λνμΈ κ·Έλνλ₯Ό λͺ¨λ μ°Ύλ λ¬Έμ , μ¦ κ·Έλν λν 쿼리 νλ‘μΈμ±μ μ’
μ’
μꡬνκΈ°λ νλ€. λ³Έ λ
Όλ¬Έμμλ λμ©λμ μ€μ κ·Έλν λ°μ΄ν°μ λν΄μ κ·Έλν λν λ¬Έμ μ κ·Έλν λν 쿼리 νλ‘μΈμ± λ¬Έμ λ₯Ό λΉ λ₯΄κ² νΈλ μκ³ λ¦¬μ¦λ€μ μ μνλ€.
첫 λ²μ§Έλ‘, λ³Έ λ
Όλ¬Έμμλ κ·Έλν λν λ¬Έμ λ₯Ό μν λΉ λ₯΄κ³ νμ₯μ± μλ μκ³ λ¦¬μ¦μ μ μνλ€. μ΄λ₯Ό μν΄ μλ³ μ κ°μ (pairwise color refinement)κ³Ό ν¨μ¨μ μΈ λ°±νΈλνΉμΌλ‘ ꡬμ±λ νλ μμν¬λ₯Ό μκ°νλ€. μ΄ νλ μμν¬ λ΄μμ μΈ κ°μ§ ν¨μ¨μ μΈ ν
ν¬λμ μ¬μ©νλ€. μ€μ κ·Έλν λ°μ΄ν°μ λν μ€νμ ν΅ν΄ λ³Έ μκ³ λ¦¬μ¦μ΄ νμ‘΄νλ κ°μ₯ λΉ λ₯Έ μκ³ λ¦¬μ¦λ€λ³΄λ€ νκ· μμ² λ°° λΉ λ¦μ 보μλ€.
λ λ²μ§Έλ‘, λ³Έ λ
Όλ¬Έμμλ κ·Έλν λν 쿼리 νλ‘μΈμ±μ μν ν¨μ¨μ μΈ μκ³ λ¦¬μ¦μ κ°λ°νλ€. λ³Έ μκ³ λ¦¬μ¦μ μ°¨μμ΄κ³Ό μ-λ μ΄λΈ λΆν¬λ₯Ό μ΄μ©ν μΈλ±μ€λ₯Ό μ΄μ©νλ€. μ€μ κ·Έλν λ°μ΄ν°μ λν μ€νμ ν΅ν΄ λ³Έ μκ³ λ¦¬μ¦μ΄ νμ‘΄νλ μκ³ λ¦¬μ¦λ€λ³΄λ€ μΈλ±μ± μκ°μμλ νμ νκ· μμ² λ°° λΉ λ₯΄κ³ , 쿼리 μ²λ¦¬ μκ°μμλ μ€λμ©λμ κ·Έλνλ€μ λν΄μ νκ· μμ λ°° λΉ λ₯΄κ² λμνλ κ²μ 보μλ€.1. Introduction 1
1.1. Background 1
1.2. Organization 3
2. Preliminaries 4
2.1. Notation 4
2.2. Problem Definitions 6
2.3. Related Work 7
3. Graph Isomorphism 9
3.1. Algorithm Overview 12
3.2. Pairwise Color Refinement and Binary Cell Mapping 13
3.3. Compressed Candidate Space 16
3.4. Backtracking and Partial Failing Sets 21
3.5. Performance Evaluation 31
3.5.1. Comparing with Existing Solutions 35
3.5.2. Effectiveness of Individual Techniques 39
3.5.3. Analysis with Varying Degrees of Similarity 42
3.5.4. Sensitivity Analysis 46
4. Graph Isomorphism Query Processing 48
4.1. Canonical Coloring 51
4.2. Index Construction 56
4.3. Query Processing 59
4.4. Performance Evaluation 63
4.4.1. Varying Number of Hops 67
4.4.2. Varying Number of Data Graphs 74
5. Conclusion 78
5.1. Summary 78
5.2. Future Directions 79
μμ½ 95λ°