Abstract
Given a set of heterogeneous devices equipped with multiple interfaces to communicate, a challenging issue is that of activating (switch-on) a subset of interfaces at each device so as to establish suitable communication connections. That is, the devices at the endpoints of each connection share at least one active interface. This is at the basis of a well-investigated model referred in the literature to as Multi-Interface networks. We consider a new variant where each interface is associated with both a cost and a profit, and also the establishment of a connection provides a profit. Moreover, each device is limited to activate at most a fixed number q of its available interfaces whereas the overall cost of the interfaces that can be activated must be kept below a predefined budget b. Within this context we consider the so-called Coverage problem where the requirement is to establish all the connections defined by the edges of an undirected graph \(G=(V,E)\), where nodes V represent the devices. We prove the problem is \(\textit{NP}\)-hard even in the basic case of \(q=2\). Then, we focus on Series-Parallel graphs, where the problem remains hard, and we design two pseudo-polynomial time optimal algorithms based on dynamic programming still for \(q=2\). Finally, we provide a fully polynomial time approximation scheme.
The work has been supported in part by the Italian MIUR PRIN 2017 Project ALGADIMAR “Algorithms, Games, and Digital Markets”, by the Italian National Group for Scientific Computation GNCS-INdAM, and by project “Robot-based computing systems”, Ricerca di Base 2018, University of Perugia, Italy.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aloisio, A., Arbib, C., Marinelli, F.: Cutting stock with no three parts per pattern: work-in-process and pattern minimization. Discrete Optim. 8, 315–332 (2011)
Aloisio, A., Arbib, C., Marinelli, F.: On LP relaxations for the pattern minimization problem. Networks 57, 247–253 (2011)
Aloisio, A., Navarra, A.: Balancing energy consumption for the establishment of multi-interface networks. In: Proceedings of the 41st International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM). LNCS, vol. 8939, pp. 102–114. Springer (2015)
Aloisio, A., Navarra, A.: Constrained connectivity in bounded X-width multi-interface networks. Algorithms 13(2), 31 (2020)
Aloisio, A., Navarra, A., Mostarda, L.: Distributing energy consumption in multi-interface series-parallel networks. In: Proceedings of the 33rd International Conference on Advanced Information Networking and Applications (AINA Workshops). Advances in Intelligent Systems and Computing, vol. 927, pp. 734–744. Springer (2019)
Angelini, P., Eades, P., Hong, S., Klein, K., Kobourov, S.G., Liotta, G., Navarra, A., Tappini, A.: Turning cliques into paths to achieve planarity. In: Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD). LNCS, vol. 11282, pp. 67–74. Springer (2018)
Athanassopoulos, S., Caragiannis, I., Kaklamanis, C., Papaioannou, E.: Energy-efficient communication in multi-interface wireless networks. Theory Comput. Syst. 52, 285–296 (2013)
Audrito, G., Bertossi, A., Navarra, A., Pinotti, C.: Maximizing the overall end-user satisfaction of data broadcast in wireless mesh networks. J. Discrete Algorithms 45, 14–25 (2017)
Caporuscio, M., Charlet, D., Issarny, V., Navarra, A.: Energetic performance of service-oriented multi-radio networks: issues and perspectives. In: Proceedings of the 6th International Workshop on Software and Performance (WOSP), pp. 42–45. ACM (2007)
Clark, B., Neufeld, E., Colbourn, C.: Maximizing the mean number of communicating vertex pairs in series-parallel networks. IEEE Trans. Reliab. 35(3), 247–251 (1986)
D’Angelo, G., Di Stefano, G., Navarra, A.: Multi-interface wireless networks: complexity and algorithms. In: Ibrahiem, S.R., El Emary, M.M. (eds.) Wireless Sensor Networks: From Theory to Applications, pp. 119–155. CRC Press, Taylor & Francis Group, Boca Raton (2013)
D’Angelo, G., Di Stefano, G., Navarra, A.: Flow problems in multi-interface networks. IEEE Trans. Comput. 63, 361–374 (2014)
D’Angelo, G., Stefano, G.D., Navarra, A.: Minimize the maximum duty in multi-interface networks. Algorithmica 63(1–2), 274–295 (2012)
Duffin, R.: Topology of series-parallel networks. J. Math. Anal. Appl. 10(2), 303–318 (1965)
Flammini, M., Moscardelli, L., Navarra, A., Pérennes, S.: Asymptotically optimal solutions for small world graphs. In: Proceedings of the 19th International Conference on Distributed Computing (DISC). LNCS, vol. 3724, pp. 414–428. Springer (2005)
Gavoille, C., Klasing, R., Kosowski, A., Kuszner, L., Navarra, A.: On the complexity of distributed graph coloring with local minimality constraints. Networks 54(1), 12–19 (2009)
Ibarra, O.H., Kim, C.E.: Fast approximation algorithms for the knapsack and sum of subset problems. J. ACM 22(4), 463–468 (1975)
Klasing, R., Kosowski, A., Navarra, A.: Cost minimization in wireless networks with a bounded and unbounded number of interfaces. Networks 53(3), 266–275 (2009)
Korenblit, M., Levit, V.: On algebraic expressions of series-parallel and Fibonacci graphs. In: Calude, C.S., Dinneen, M.J., Vajnovszki, V. (eds.) Discrete Mathematics and Theoretical Computer Science, pp. 215–224. Springer, Heidelberg (2003)
Kosowski, A., Navarra, A., Pajak, D., Pinotti, C.: Maximum matching in multi-interface networks. Theoret. Comput. Sci. 507, 52–60 (2013)
Kosowski, A., Navarra, A., Pinotti, M.: Exploiting multi-interface networks: connectivity and cheapest paths. Wireless Netw. 16(4), 1063–1073 (2010)
Martello, S., Toth, P.: Knapsack Problems. Biddles Ltd., Guildford (1990)
Navarra, A., Pinotti, C.M.: Online knapsack of unknown capacity: how to optimize energy consumption in smartphones. Theoret. Comput. Sci. 697, 98–109 (2017)
Valdes, J., Tarjan, R., Lawler, E.: The recognition of series parallel digraphs. In: Proceedings of the 11th Annual ACM Symposium on Theory of Computing (STOC), pp. 1–12. ACM (1979)
Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms. Cambridge University Press, New York (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Aloisio, A., Navarra, A. (2020). Budgeted Constrained Coverage on Series-Parallel Multi-interface Networks. In: Barolli, L., Amato, F., Moscato, F., Enokido, T., Takizawa, M. (eds) Advanced Information Networking and Applications. AINA 2020. Advances in Intelligent Systems and Computing, vol 1151. Springer, Cham. https://doi.org/10.1007/978-3-030-44041-1_41
Download citation
DOI: https://doi.org/10.1007/978-3-030-44041-1_41
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44040-4
Online ISBN: 978-3-030-44041-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)