Random walk with restart over dynamic graphs

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Title: Random walk with restart over dynamic graphs
Authors: Yu, W
McCann, J
Item Type: Conference Paper
Abstract: Random Walk with Restart (RWR) is an appealing measure of proximity between nodes based on graph structures. Since real graphs are often large and subject to minor changes, it is prohibitively expensive to recompute proximities from scratch. Previous methods use LU decomposition and degree reordering heuristics, entailing O(|V |3) time and O(|V |2) memory to compute all (|V |2) pairs of node proximities in a static graph. In this paper, a dynamic scheme to assess RWR proximities is proposed: (1) For unit update, we characterize the changes to all-pairs proximities as the outer product of two vectors. We notice that the multiplication of an RWR matrix and its transition matrix, unlike traditional matrix multiplications, is commutative. This can greatly reduce the computation of all-pairs proximities from O(|V |3) to O(|Δ|) time for each update without loss of accuracy, where |Δ| (≪ |V |2) is the number of affected proximities. (2) To avoid O(|V |2) memory for all pairs of outputs, we also devise efficient partitioning techniques for our dynamic model, which can compute all pairs of proximities segment-wisely within O(l|V |) memory and O(⌈ |V | l ⌉) I/O costs, where 1 ≤ l ≤ |V | is a user-controlled trade-off between memory and I/O costs. (3) For bulk updates, we also devise aggregation and hashing methods, which can discard many unnecessary updates further and handle chunks of unit updates simultaneously. Our experimental results on various datasets demonstrate that our methods can be 1-2 orders of magnitude faster than other competitors while securing scalability and exactness.
Issue Date: 2-Feb-2017
Date of Acceptance: 12-Dec-2016
URI: http://hdl.handle.net/10044/1/45323
DOI: https://dx.doi.org/10.1109/ICDM.2016.0070
ISBN: 9781509054725
ISSN: 2374-8486
Publisher: IEEE
Start Page: 589
End Page: 598
Journal / Book Title: 2016 IEEE 16th International Conference on Data Mining (ICDM)
Copyright Statement: © 2017 IEEE.
Sponsor/Funder: NEC Corporation
NEC Research Institute Inc
Funder's Grant Number: N/A
Yuichi Nakamura
Conference Name: 2016 IEEE 16th International Conference on Data Mining (ICDM)
Publication Status: Published
Start Date: 2016-12-12
Finish Date: 2016-12-15
Appears in Collections:Faculty of Engineering

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