Sketch-based Randomized Algorithms for Dynamic Graph Regression

A well-known problem in data science and machine learning is linear regression, which is recently extended to dynamic graphs. Existing exact algorithms for updating the solution of dynamic graph regression problem require at least a linear time (in terms of n: the size of the graph). However, this time complexity might be intractable in practice. In the current paper, we utilize subsampled randomized Hadamard transform and CountSketch to propose the first randomized algorithms. Suppose that we are given an n× m matrix embedding M of the graph, where m ≪ n. Let r be the number of samples required for a guaranteed approximation error, which is a sublinear function of n. Our first algorithm reduces time complexity of pre-processing to O(n(m + 1) + 2n(m + 1) _2(r + 1) + rm^2). Then after an edge insertion or an edge deletion, it updates the approximate solution in O(rm) time. Our second algorithm reduces time complexity of pre-processing to O ( nnz(M) (n/ϵ) + m^3 ^2 m + m^2 (1/ϵ) ), where nnz(M) is the number of nonzero elements of M. Then after an edge insertion or an edge deletion or a node insertion or a node deletion, it updates the approximate solution in O(qm) time, with q=O(m^2/ϵ^2).


page 1

page 2

page 3

page 4


Advice Complexity bounds for Online Delayed F-Node-, H-Node- and H-Edge-Deletion Problems

Let F be a fixed finite obstruction set of graphs and G be a graph revea...

Semi-dynamic Algorithms for Strongly Chordal Graphs

There is an extensive literature on dynamic algorithms for a large numbe...

Efficient Strongly Polynomial Algorithms for Quantile Regression

Linear Regression is a seminal technique in statistics and machine learn...

Fast and Efficient Matching Algorithm with Deadline Instances

Online weighted matching problem is a fundamental problem in machine lea...

Sampling an Edge in Sublinear Time Exactly and Optimally

Sampling edges from a graph in sublinear time is a fundamental problem a...

Large Scale Constrained Linear Regression Revisited: Faster Algorithms via Preconditioning

In this paper, we revisit the large-scale constrained linear regression ...

A Note on Improved Results for One Round Distributed Clique Listing

In this note, we investigate listing cliques of arbitrary sizes in bandw...

Please sign up or login with your details

Forgot password? Click here to reset