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.
This work was partially supported by Berlin Mathematical School, by DFG research center Matheon and by the DFG Focus Program 1307 within the project “Algorithm Engineering for Real-time Scheduling and Routing”.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Leung, J.Y.T., Tam, T.W., Wong, C.S., Young, G.H.: Routing messages with release time and deadline constraints. Journal of Parallel and Distributed Computing 31, 65–76 (1995)
Leung, J.Y.T., Tam, T.W., Wong, C.S., Young, G.H.: Online routing of real-time messages. Journal of Parallel and Distributed Computing 34, 211–217 (1996)
Leung, J.Y.-T.: Handbook of Scheduling: Algorithms, Models and Performance Analysis. Chapman and Hall/CRC, Boca Raton (2004)
Leighton, F.: Methods for message routing in parallel machines. In: Proceedings of the ACM Symposium on the Theory of Computing, pp. 77–96 (1992)
Hall, A., Hippler, S., Skutella, M.: Multicommodity flows over time: Efficient algorithms and complexity. Theoretical Computer Science 379, 387–404 (2007)
Williamson, D.P., Hall, L.A., Hoogeveen, J.A., Hurkens, C.A.J., Lenstra, J.K., Sevast’janov, A.V., Shmoys, D.B.: Short shop schedules. Operations Research 45, 288–294 (1997)
Feige, U., Scheideler, C.: Improved bounds for acyclic job shop scheduling. Combinatorica 3(22), 361–399 (2002)
Czumaj, A., Scheideler, C.: A new algorithmic approach to the general Lovász Local Lemma with applications to scheduling and satisfiability problems. In: Proc. of the thirty-second annual ACM symposium on Theory of computing, Portland, USA, pp. 38–47 (2000)
Leigthon, F.T., Maggs, B.M., Rao, S.B.: Packet routing and job shop scheduling in O(congestion+dilation) steps. Combinatorica 14, 167–186 (1994)
Leigthon, F.T., Maggs, B.M., Richa, A.: Fast algorithms for finding O(congestion+dilation) packet routing schedules. Combinatorica 19, 375–401 (1999)
Busch, C., Magdon-Ismail, M., Mavronicolas, M.: Universal bufferless packet switching. SIAM Journal on Computing 37, 1139–1162 (2007)
Srinivasan, A., Teo, C.-P.: A constant-factor approximation algorithm for packet routing and balancing local vs. global criteria. SIAM Journal on Computing 30(6), 2051–2068 (2001)
Fleischer, L., Skutella, M.: Quickest flows over time. SIAM Journal on Computing 36, 1600–1630 (2007)
Garey, M.R., Johnson, D.S.: Computers and Intractability. W. H. Freeman and Co., New York (1979)
Grtschel, M., Lovsz, L., Schrijver, A.: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2), 169–197 (1981)
Karp, R.M., Leigthon, F.T., Rivest, R.L., Thompson, C.D., Vazirani, U.V., Vazirani, V.V.: Global wire routing in two-dimensional arrays. Algorithmica 2, 113–129 (1987)
Hassin, R.: Approximation schemes for the restricted shortest path problem. Math. Oper. Research 17, 36–42 (1992)
Lorenz, D.H., Raz, D.: A simple efficient approximation scheme for the restricted shortest path problem. Oper. Res. Letters 28, 213–219 (2001)
Phillips, C.A.: The network inhibition problem. In: Proc. of the 25th Annual ACM Symposium on the Theory of Computing, San Diego, CA, pp. 776–785 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Koch, R., Peis, B., Skutella, M., Wiese, A. (2009). Real-Time Message Routing and Scheduling. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-03685-9_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03684-2
Online ISBN: 978-3-642-03685-9
eBook Packages: Computer ScienceComputer Science (R0)