Abstract
We study the algorithmic problem of coordinating transmissions in a wireless network where radio interference constrains concurrent transmissions on wireless links. We focus on pairwise conflicts between the links; these can be described as a conflict graph. Associated with the conflict graph are two fundamental network coordination tasks: (a) finding a nonconflicting set of links with the maximum total weight, and (b) finding a link schedule with the minimum total length. Our work shows that two assumptions on the geometric structure of conflict graphs suffice to achieve polynomial-time constant-factor approximations: (i) bounded density of devices, and (ii) bounded range of interference. We also show that these assumptions are not sufficient to obtain a polynomial-time approximation scheme for either coordination task.
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References
Jain, K., Padhye, J., Padmanabhan, V.N., Qiu, L.: Impact of interference on multi-hop wireless network performance. Wireless Networks 11(4), 471–487 (2005)
Jansen, K.: Approximate strong separation with application in fractional graph coloring and preemptive scheduling. Theoretical Computer Science 302(1–3), 239–256 (2003)
Young, N.E.: Sequential and parallel algorithms for mixed packing and covering. In: Proc. 42nd Annual Symposium on Foundations of Computer Science FOCS, Las Vegas, NV, USA, October 2001, pp. 538–546. IEEE Computer Society Press, Los Alamitos (2001)
Håstad, J.: Clique is hard to approximate within n 1 − ε. Acta Mathematica 182, 105–142 (1999)
Khot, S.: Improved inapproximability results for MaxClique, chromatic number and approximate graph coloring. In: Proc. 42nd Annual Symposium on Foundations of Computer Science FOCS, Las Vegas, NV, USA, October 2001, pp. 600–609. IEEE Computer Society Press, Los Alamitos (2001)
Lund, C., Yannakakis, M.: On the hardness of approximating minimization problems. Journal of the ACM 41(5), 960–981 (1994)
Goldsmith, A.: Wireless Communications. Cambridge University Press, Cambridge, UK (2005)
Krishnamachari, B.: Networking Wireless Sensors. Cambridge University Press, Cambridge, UK (2005)
Suomela, J.: Approximability of identifying codes and locating-dominating codes. Information Processing Letters 103(1), 28–33 (2007)
Doyle, P.G., Snell, J.L.: Random Walks and Electric Networks. The Mathematical Association of America, Washington, DC, USA (1984)
Halldórsson, M.M.: Approximations of independent sets in graphs. In: Jansen, K., Rolim, J.D.P. (eds.) APPROX 1998. LNCS, vol. 1444, pp. 1–13. Springer, Heidelberg (1998)
Halldórsson, M.M.: Approximations of weighted independent set and hereditary subset problems. Journal of Graph Algorithms and Applications 4(1), 1–16 (2000)
Erlebach, T., Jansen, K., Seidel, E.: Polynomial-time approximation schemes for geometric intersection graphs. SIAM Journal on Computing 34(6), 1302–1323 (2005)
Hochbaum, D.S., Maass, W.: Approximation schemes for covering and packing problems in image processing and VLSI. Journal of the ACM 32(1), 130–136 (1985)
Hunt III, H.B., Marathe, M.V., Radhakrishnan, V., Ravi, S.S., Rosenkrantz, D.J., Stearns, R.E.: NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs. Journal of Algorithms 26(2), 238–274 (1998)
Khanna, S., Motwani, R., Sudan, M., Vazirani, U.: On syntactic versus computational views of approximability. SIAM Journal on Computing 28(1), 164–191 (1999)
Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. Journal of Computer and System Sciences 43(3), 425–440 (1991)
Chvátal, V., Ebenegger, C.: A note on line digraphs and the directed max-cut problem. Discrete Applied Mathematics 29(2–3), 165–170 (1990)
Erlebach, T., Jansen, K.: Conversion of coloring algorithms into maximum weight independent set algorithms. Discrete Applied Mathematics 148(1), 107–125 (2005)
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Kaski, P., Penttinen, A., Suomela, J. (2007). Coordinating Concurrent Transmissions: A Constant-Factor Approximation of Maximum-Weight Independent Set in Local Conflict Graphs . In: Kranakis, E., Opatrny, J. (eds) Ad-Hoc, Mobile, and Wireless Networks. ADHOC-NOW 2007. Lecture Notes in Computer Science, vol 4686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74823-6_6
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DOI: https://doi.org/10.1007/978-3-540-74823-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74822-9
Online ISBN: 978-3-540-74823-6
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