Sliding Window Temporal Graph Coloring

Mertzios, G.B.; Molter, H.; Zamaraev, V.

Abstract

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).

Citation

Mertzios, G., Molter, H., & Zamaraev, V. (2023, January). Sliding Window Temporal Graph Coloring. Presented at 33rd AAAI Conference on Artificial Intelligence (AAAI 2019)., Honolulu, Hawaii, USA

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 33rd AAAI Conference on Artificial Intelligence (AAAI 2019).
• Start Date: Jan 27, 2023
• End Date: Feb 1, 2019
• Acceptance Date: Oct 31, 2018
• Online Publication Date: Jul 17, 2019
• Publication Date: Jul 17, 2019
• Deposit Date: Nov 14, 2018
• Publicly Available Date: Nov 15, 2018
• Volume: 33
• Pages: 7667-7674
• Series Number: 1
• Series ISSN: 2159-5399,2374-3468
• Book Title: Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence.
• DOI: https://doi.org/10.1609/aaai.v33i01.33017667
• Public URL: https://durham-repository.worktribe.com/output/1142773
• Publisher URL: https://doi.org/10.1609/aaai.v33i01.33017667
• Related Public URLs: https://arxiv.org/abs/1811.04753