Publication Date
2021
Journal or Book Title
Algorithmica
Abstract
Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as k-center, k-median, and k-means. Such algorithms need to be both time and and space efcient. In this paper, we address the problem of correlation clustering in the dynamic data stream model. The stream consists of updates to the edge weights of a graph on n nodes and the goal is to find a node-partition such that the end-points of negative-weight edges are typically in diferent clusters whereas the end-points of positive-weight edges are typically in the same cluster. We present polynomial-time, O(n ⋅ polylog n)-space approximation algorithms for natural problems that arise. We frst develop data structures based on linear sketches that allow the “quality” of a given node-partition to be measured. We then combine these data structures with convex programming and sampling techniques to solve the relevant approximation problem. Unfortunately, the standard LP and SDP formulations are not obviously solvable in O(n ⋅ polylog n)-space. Our work presents space-efcient algorithms for the convex programming required, as well as approaches to reduce the adaptivity of the sampling.
DOI
https://doi.org/10.1007/s00453-021-00816-9
License
UMass Amherst Open Access Policy
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Ahn, Kook Jin; Cormode, Graham; Guha, Sudipto; McGregor, Andrew; and Wirth, Anthony, "Correlation Clustering in Data Streams" (2021). Algorithmica. 1344.
https://doi.org/10.1007/s00453-021-00816-9