Real-Time Message Routing and Scheduling

Authors:
Ronald Koch;Britta Peis;Martin Skutella;Andreas Wiese
Affiliations:
Institut für Mathematik, TU Berlin, Berlin, Germany 10623;Institut für Mathematik, TU Berlin, Berlin, Germany 10623;Institut für Mathematik, TU Berlin, Berlin, Germany 10623;Institut für Mathematik, TU Berlin, Berlin, Germany 10623
Venue:
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2009

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Abstract

Exchanging messages between nodes of a network (e.g., embedded computers) is a fundamental issue in real-time systems involving critical routing and scheduling decisions. In order for messages to arrive on time, one has to determine a suitable (short) origin-destination path for each message and resolve conflicts between messages whose paths share a communication link of the network. We provide efficient routing strategies yielding origin-destination paths of bounded dilation and congestion. In particular, we can give good a priori guarantees on the time required to send a given set of messages which, under certain reasonable conditions, implies that all messages can be scheduled to reach their destination on time. Our algorithm uses a path-based LP-relaxation and iterative rounding. Finally, for message routing along a directed path (which is already $\mathcal{NP}$-hard), we identify a natural class of instances for which a simple scheduling heuristic yields provably optimal solutions.