Space Reduction for Extreme Aggregation of Data Stream over Time-Based Sliding Window

Monitoring and interpretation of changing patterns is a task of paramount importance for data mining applications in dynamic environments. While there is much research in adapting patterns in the presence of drift or shift, there is less research on how to maintain an overview of pattern changes over time. A major challenge is summarizing changes in an effective way, so that the nature of change can be understood by the user, while the demand on resources remains low. To this end, the authors propose FINGERPRINT, an environment for the summarization of cluster evolution. Cluster changes are captured into an “evolution graph,” which is then summarized based on cluster similarity into a fingerprint of evolution by merging similar clusters. The authors propose a batch summarization method that traverses and summarizes the Evolution Graph as a whole and an incremental method that is applied during the process of cluster transition discovery. They present experiments on different data streams and discuss the space reduction and information preservation achieved by the two methods.

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Sliding Window Temporal Graph Coloring

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33017667 ◽

2019 ◽

Vol 33 ◽

pp. 7667-7674 ◽

Cited By ~ 2

Author(s):

George B. Mertzios ◽

Hendrik Molter ◽

Viktor Zamaraev

Keyword(s):

Graph Coloring ◽

Time Window ◽

Linear Time ◽

Sliding Window ◽

Planning And Scheduling ◽

Coloring Problem ◽

Wide Range ◽

Temporal Graph ◽

Changes Over Time ◽

Over Time

Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static graphs, which often stand in stark contrast to practice where data is inherently dynamic and subject to discrete changes over time. A temporal graph is a graph whose edges are assigned a set of integer time labels, indicating at which discrete time steps the edge is active. In this paper we present a natural temporal extension of the classical graph coloring problem. Given a temporal graph and a natural number ∆, we ask for a coloring sequence for each vertex such that (i) in every sliding time window of ∆ consecutive time steps, in which an edge is active, this edge is properly colored (i.e. its endpoints are assigned two different colors) at least once during that time window, and (ii) the total number of different colors is minimized. This sliding window temporal coloring problem abstractly captures many realistic graph coloring scenarios in which the underlying network changes over time, such as dynamically assigning communication channels to moving agents. We present a thorough investigation of the computational complexity of this temporal coloring problem. More specifically, we prove strong computational hardness results, complemented by efficient exact and approximation algorithms. Some of our algorithms are linear-time fixed-parameter tractable with respect to appropriate parameters, while others are asymptotically almost optimal under the Exponential Time Hypothesis (ETH).

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