Taming Computational Complexity: Efficient and Parallel SimRank Optimizations on Undirected Graphs

Yu, Weiren; Lin, Xuemin; Le, Jiajin

doi:10.1007/978-3-642-14246-8_29

Cited by 10 publications

(19 citation statements)

References 21 publications

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“…The key idea in our optimization is to maximally use the adjacency matrix A to characterize the P-Rank similarity S as a power series in a function form like S = It is worth noting that SimRank over undirected graphs is a special case of the more general P-Rank when λ = 1 and C in = C out . In contrast to the O(n 3 + Kn 2 )-time of SimRank optimization over undirected graphs in our early work [14], this work further optimizes P-Rank time in O(n 3 ) with no need for iteration. To show Theorem 3, we first characterize P-Rank elegantly on undirected graphs.…”

Section: An Efficient Algorithm For P-rank Estimating On Undirected Gmentioning

confidence: 90%

ASAP : Towards Accurate, Stable and Accelerative Penetrating-Rank Estimation on Large Graphs

Yang

et al. 2011

Web-Age Information Management

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Abstract. Pervasive web applications increasingly require a measure of similarity among objects. Penetrating-Rank (P-Rank) has been one of the promising link-based similarity metrics as it provides a comprehensive way of jointly encoding both incoming and outgoing links into computation for emerging applications. In this paper, we investigate P-Rank efficiency problem that encompasses its accuracy, stability and computational time. (1) We provide an accuracy estimate for iteratively computing P-Rank. A symmetric problem is to find the iteration number K needed for achieving a given accuracy ǫ. (2) We also analyze the stability of P-Rank, by showing that small choices of the damping factors would make P-Rank more stable and wellconditioned. (3) For undirected graphs, we also explicitly characterize the P-Rank solution in terms of matrices. This results in a novel non-iterative algorithm, termed ASAP , for efficiently computing P-Rank, which improves the CPU time from O(n 4 ) to O n 3 . Using real and synthetic data, we empirically verify the effectiveness and efficiency of our approaches.

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Section: An Efficient Algorithm For P-rank Estimating On Undirected Gmentioning

confidence: 90%

ASAP : Towards Accurate, Stable and Accelerative Penetrating-Rank Estimation on Large Graphs

Yang

et al. 2011

Web-Age Information Management

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“…All P-Rank iterations with k > 0 can be expressed as a series of iterations converging to the theoretical similarity score. Based on the optimization devised by Yu et al [36], the computational complexity of this measure has the upper bound O(n 3 + Kn 2 ).…”

Section: Network Similarity (S Net )mentioning

confidence: 99%

A Structural-Lexical Measure of Semantic Similarity for Geo-Knowledge Graphs

Ballatore

Bertolotto

Wilson

2015

IJGI

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Graphs have become ubiquitous structures to encode geographic knowledge online. The Semantic Web's linked open data, folksonomies, wiki websites and open gazetteers can be seen as geo-knowledge graphs, that is labeled graphs whose vertices represent geographic concepts and whose edges encode the relations between concepts. To compute the semantic similarity of concepts in such structures, this article defines the network-lexical similarity measure (NLS). This measure estimates similarity by combining two complementary sources of information: the network similarity of vertices and the semantic similarity of the lexical definitions. NLS is evaluated on the OpenStreetMap Semantic Network, a crowdsourced geo-knowledge graph that describes geographic concepts. The hybrid approach outperforms both network and lexical measures, obtaining very strong correlation with the similarity judgments of human subjects.

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“…There has also been work on other similarity optimization (e.g., [5,6,15,18,20,22,24,25]). Lizorkin et al [18] proposed an interesting memoization approach to improve the computation of SimRank from O(Kn 4 ) to O(Kn 3 ).…”

Section: Related Workmentioning

confidence: 99%

“…A notion of the weighted and evidencebased SimRank is proposed by Antonellis et al [1], yielding better query rewrites for sponsored search. He et al [6] and Yu et al [24] show interesting approaches to paralleling the computation of SimRank.…”

Section: Related Workmentioning

confidence: 99%

“…We can see that the items sugar and egg are similar as they are purchased by the same person (A). In spite of its worldwide popularity [1,4,6,18,24,27], SimRank has the "limited information problem" -it only takes incoming edges into account while ignoring outgoing links [26]. For instance, person (A) and (B) have the SimRank score zero as they have no incoming edges.…”

Section: Introductionmentioning

confidence: 99%

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On the Efficiency of Estimating Penetrating Rank on Large Graphs

Lin

et al. 2012

Lecture Notes in Computer Science

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Abstract. P-Rank (Penetrating Rank) has been suggested as a useful measure of structural similarity that takes account of both incoming and outgoing edges in ubiquitous networks. Existing work often utilizes memoization to compute PRank similarity in an iterative fashion, which requires cubic time in the worst case. Besides, previous methods mainly focus on the deterministic computation of P-Rank, but lack the probabilistic framework that scales well for large graphs. In this paper, we propose two efficient algorithms for computing P-Rank on large graphs. The first observation is that a large body of objects in a real graph usually share similar neighborhood structures. By merging such objects with an explicit low-rank factorization, we devise a deterministic algorithm to compute P-Rank in quadratic time. The second observation is that by converting the iterative form of P-Rank into a matrix power series form, we can leverage the random sampling approach to probabilistically compute P-Rank in linear time with provable accuracy guarantees. The empirical results on both real and synthetic datasets show that our approaches achieve high time efficiency with controlled error and outperform the baseline algorithms by at least one order of magnitude.

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Taming Computational Complexity: Efficient and Parallel SimRank Optimizations on Undirected Graphs

Cited by 10 publications

References 21 publications

ASAP : Towards Accurate, Stable and Accelerative Penetrating-Rank Estimation on Large Graphs

ASAP : Towards Accurate, Stable and Accelerative Penetrating-Rank Estimation on Large Graphs

A Structural-Lexical Measure of Semantic Similarity for Geo-Knowledge Graphs

On the Efficiency of Estimating Penetrating Rank on Large Graphs

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