Abstract
This paper studies the aggregation of messages in networks that consist of a chain of nodes, and each message is time-constrained such that it needs to be aggregated during a given time interval, called its due interval. The objective is to minimize the maximum cost incurred at any node, which is for example a concern in wireless sensor networks, where it is crucial to distribute the energy consumption as equally as possible. First, we settle the complexity of this problem by proving its NP-hardness, even for the case of unit length due intervals. Second, we give a QPTAS, which we extend to a PTAS for the special case that the lengths of the due intervals are constants. This is in particular interesting, since we prove that this problem becomes APX-hard if we consider tree networks instead of chain networks, even for the case of unit length due intervals. Specifically, we show that it cannot be approximated within 4/3 − ε for any ε> 0 , unless P=NP.
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
Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless sensor networks: a survey. Comput. Netw. 38(4), 393–422 (2002)
Becchetti, L., Korteweg, P., Marchetti-Spaccamela, A., Skutella, M., Stougie, L., Vitaletti, A.: Latency constrained aggregation in sensor networks. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 88–99. Springer, Heidelberg (2006)
Brito, C., Koutsoupias, E., Vaya, S.: Competitive analysis of organization networks or multicast acknowledgement: how much to wait? In: Proc. of the 15th annual ACM-SIAM symposium on Discrete algorithms (SODA), pp. 627–635 (2004)
Even, G., Levi, R., Rawitz, D., Schieber, B., Shahar, S., Sviridenko, M.: Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs. ACM Trans. Alg. 4(3) (2008)
Gaur, D.R., Ibaraki, T., Krishnamurti, R.: Constant ratio approximation algorithms for the rectangle stabbing problem and the rectilinear partitioning problem. J. Algorithms 43(1), 138–152 (2002)
Gijswijt, D., Jost, V., Queyranne, M.: Clique partitioning of interval graphs with submodular costs on the cliques. RAIRO - Operations Research 41(3), 275–287 (2007)
Glasser, C., Schmitz, H., Reitwiessner, C.: Multiobjective disk cover admits a PTAS. In: Proc. of the 19th International Symposium on Algorithms and Computation (ISSAC) (2008)
Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Annals of Discrete Mathematics, vol. 57. North-Holland Publishing Co, Amsterdam (2004)
Hassin, R., Megiddo, N.: Approximation algorithms for hitting objects with straight lines. Discrete Applied Mathematics 30(1), 29–42 (1991)
Hochbaum, D.S., Maass, W.: Approximation schemes for covering and packing problems in image processing and VLSI. J. ACM 32(1), 130–136 (1985)
Khanna, S., Naor, J(S.), Raz, D.: Control message aggregation in group communication protocols. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 135–146. Springer, Heidelberg (2002)
Korteweg, P., Marchetti-Spaccamela, A., Stougie, L., Vitaletti, A.: Data aggregation in sensor networks: Balancing communication and delay costs. In: Prencipe, G., Zaks, S. (eds.) SIROCCO 2007. LNCS, vol. 4474, pp. 139–150. Springer, Heidelberg (2007)
Krishnamachari, B., Estrin, D., Wicker, S.B.: The impact of data aggregation in wireless sensor networks. In: Proc. of the 29th International Conference on Distributed Computing Systems (ICDCS), pp. 575–578 (2002)
Lenstra, J.K., Shmoys, D.B., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Math. Program. 46(3), 259–271 (1990)
Oswald, Y.A., Schmid, S., Wattenhofer, R.: Tight bounds for delay-sensitive aggregation. In: Proc. of the 27th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 195–202 (2008)
Papadimitriou, C.H.: Computational aspects of organization theory (extended abstract). In: Díaz, J. (ed.) ESA 1996. LNCS, vol. 1136, pp. 559–564. Springer, Heidelberg (1996)
Papadimitriou, C.H., Yannakakis, M.: On the approximability of trade-offs and optimal access of web sources. In: Proc. of the 41st Annual Symposium on Foundations of Computer Science (FOCS), pp. 86–92 (2000)
Yu, Y., Krishnamachari, B., Prasanna, V.K.: Energy-latency tradeoffs for data gathering in wireless sensor networks. In: Proc. of the 23rd Conference of the IEEE Communications Society (INFOCOM) (2004)
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
Nonner, T., Souza, A. (2009). Latency Constrained Aggregation in Chain Networks Admits a PTAS. In: Goldberg, A.V., Zhou, Y. (eds) Algorithmic Aspects in Information and Management. AAIM 2009. Lecture Notes in Computer Science, vol 5564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02158-9_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-02158-9_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02157-2
Online ISBN: 978-3-642-02158-9
eBook Packages: Computer ScienceComputer Science (R0)